diff --git a/paddle/phi/kernels/gpu/determinant_grad_kernel.cu b/paddle/phi/kernels/gpu/determinant_grad_kernel.cu
index cce12a87fac72f5ac6edbbeb74de9fe3ae9ede09..f3187d5fefb5191a3d42cfa6f94a4fdeb035a7e1 100644
--- a/paddle/phi/kernels/gpu/determinant_grad_kernel.cu
+++ b/paddle/phi/kernels/gpu/determinant_grad_kernel.cu
@@ -21,5 +21,6 @@ PD_REGISTER_KERNEL(determinant_grad,
                    GPU,
                    ALL_LAYOUT,
                    phi::DeterminantGradKernel,
+                   phi::dtype::float16,
                    float,
                    double) {}
diff --git a/paddle/phi/kernels/gpu/determinant_kernel.cu b/paddle/phi/kernels/gpu/determinant_kernel.cu
index 25184083873952638a1f84d8d4b66262363ca9c6..58e27e3ce4abdaebd2411c97daf85f92638a8c69 100644
--- a/paddle/phi/kernels/gpu/determinant_kernel.cu
+++ b/paddle/phi/kernels/gpu/determinant_kernel.cu
@@ -17,5 +17,10 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/impl/determinant_kernel_impl.h"
 
-PD_REGISTER_KERNEL(
-    determinant, GPU, ALL_LAYOUT, phi::DeterminantKernel, float, double) {}
+PD_REGISTER_KERNEL(determinant,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::DeterminantKernel,
+                   phi::dtype::float16,
+                   float,
+                   double) {}
diff --git a/paddle/phi/kernels/impl/determinant_grad_kernel_impl.h b/paddle/phi/kernels/impl/determinant_grad_kernel_impl.h
index 3f463e1d9e0644f62a0b3e8508f333731c466922..4d58698c64d228d34d35b867f58134cee4ea7db9 100644
--- a/paddle/phi/kernels/impl/determinant_grad_kernel_impl.h
+++ b/paddle/phi/kernels/impl/determinant_grad_kernel_impl.h
@@ -15,8 +15,10 @@
 #pragma once
 
 #include "glog/logging.h"
+#include "paddle/phi/common/amp_type_traits.h"
 
 #include "paddle/phi/core/tensor_utils.h"
+#include "paddle/phi/kernels/cast_kernel.h"
 #include "paddle/phi/kernels/determinant_grad_kernel.h"
 #include "paddle/phi/kernels/elementwise_multiply_kernel.h"
 #include "paddle/phi/kernels/empty_kernel.h"
@@ -26,7 +28,6 @@
 #include "paddle/phi/kernels/funcs/matrix_inverse.h"
 #include "paddle/phi/kernels/funcs/unsqueeze.h"
 #include "paddle/phi/kernels/transpose_kernel.h"
-
 namespace phi {
 namespace detail {
 
@@ -113,6 +114,11 @@ void DeterminantGradKernel(const Context& dev_ctx,
     return;
   }
 
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+  auto origin_dt = std::is_same<phi::dtype::float16, T>::value
+                       ? DataType::FLOAT16
+                       : DataType::BFLOAT16;
+
   // The matrix is invertible
   // let |A| = Determinant(A)
   // Ref to https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf
@@ -123,16 +129,22 @@ void DeterminantGradKernel(const Context& dev_ctx,
   DenseTensor inverse_A;
   // A must be square matrices!
   inverse_A.Resize(x.dims());
-  dev_ctx.template Alloc<T>(&inverse_A);
+  dev_ctx.template Alloc<MPType>(&inverse_A);
 
-  phi::funcs::MatrixInverseFunctor<Context, T> mat_inv;
-  mat_inv(dev_ctx, x, &inverse_A);
+  phi::funcs::MatrixInverseFunctor<Context, MPType> mat_inv;
+  if (!std::is_same<MPType, T>::value) {
+    mat_inv(dev_ctx,
+            phi::Cast<T, Context>(dev_ctx, x, DataType::FLOAT32),
+            &inverse_A);
+  } else {
+    mat_inv(dev_ctx, x, &inverse_A);
+  }
 
   VLOG(3) << "inverse(A) dims: " << inverse_A.dims();
 
   // Second: inverse(A).transpose(-2, -1)
   DenseTensor transpose_inverse_A =
-      phi::TransposeLast2Dim<T>(dev_ctx, inverse_A);
+      phi::TransposeLast2Dim<MPType>(dev_ctx, inverse_A);
 
   VLOG(3) << "(dA * |A|).transpose(-2, -1) dims: "
           << transpose_inverse_A.dims();
@@ -147,7 +159,15 @@ void DeterminantGradKernel(const Context& dev_ctx,
   VLOG(3) << "unsqueezed(dA * |A|) dims: " << unsqueeze2.dims();
 
   // Finally: unsqueeze(dA * |A|) * inverse(A)
-  auto res = phi::Multiply<T>(dev_ctx, unsqueeze2, transpose_inverse_A);
+  DenseTensor res;
+  if (!std::is_same<MPType, T>::value) {
+    res = phi::Multiply<T>(
+        dev_ctx,
+        unsqueeze2,
+        phi::Cast<MPType, Context>(dev_ctx, transpose_inverse_A, origin_dt));
+  } else {
+    res = phi::Multiply<T>(dev_ctx, unsqueeze2, transpose_inverse_A);
+  }
 
   VLOG(3) << "unsqueeze(dA * |A|) * inverse(A) dims: " << res.dims();
 
diff --git a/paddle/phi/kernels/impl/determinant_kernel_impl.h b/paddle/phi/kernels/impl/determinant_kernel_impl.h
index 36e47c78c832c10fc8613604c47239508f44e725..3c437ad659c43ac3c7556b149e0f13cbcffe65d5 100644
--- a/paddle/phi/kernels/impl/determinant_kernel_impl.h
+++ b/paddle/phi/kernels/impl/determinant_kernel_impl.h
@@ -21,6 +21,7 @@
 #include <vector>
 
 #include "glog/logging.h"
+#include "paddle/phi/common/amp_type_traits.h"
 
 #include "paddle/phi/core/enforce.h"
 #include "paddle/phi/core/tensor_utils.h"
@@ -31,6 +32,13 @@ namespace detail {
 template <typename T>
 class EigenMatrix {};
 
+template <>
+class EigenMatrix<phi::dtype::float16> {
+ public:
+  using MatrixType =
+      Eigen::Matrix<phi::dtype::float16, Eigen::Dynamic, Eigen::Dynamic>;
+};
+
 template <>
 class EigenMatrix<float> {
  public:
@@ -74,6 +82,7 @@ struct DeterminantFunctor {
     std::vector<T> input_vec;
     std::vector<T> output_vec;
     phi::TensorToVector(input, dev_ctx, &input_vec);
+    using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
     for (int64_t i = 0; i < batch_count; ++i) {  // maybe can be parallel
       auto begin_iter = input_vec.begin() + i * rank * rank;
       auto end_iter = input_vec.begin() + (i + 1) * rank * rank;
@@ -85,7 +94,8 @@ struct DeterminantFunctor {
           matrix(i, j) = sub_vec[rank * i + j];
         }
       }
-      output_vec.push_back(matrix.determinant());
+      output_vec.push_back(
+          static_cast<T>(matrix.template cast<MPType>().determinant()));
     }
     phi::TensorFromVector(output_vec, dev_ctx, output);
   }
diff --git a/python/paddle/fluid/tests/unittests/test_determinant_op.py b/python/paddle/fluid/tests/unittests/test_determinant_op.py
index ade000cda8712e5ab99e9fd984be4f9eb358a64f..8e50f0c5552ec35124840e984a5ed7b4770817f8 100644
--- a/python/paddle/fluid/tests/unittests/test_determinant_op.py
+++ b/python/paddle/fluid/tests/unittests/test_determinant_op.py
@@ -50,6 +50,14 @@ class TestDeterminantOpCase1(TestDeterminantOp):
         self.target = np.linalg.det(self.case)
 
 
+class TestDeterminantOpCase1FP16(TestDeterminantOp):
+    def init_data(self):
+        np.random.seed(0)
+        self.case = np.random.rand(10, 10).astype(np.float16)
+        self.inputs = {'Input': self.case}
+        self.target = np.linalg.det(self.case.astype(np.float32))
+
+
 class TestDeterminantOpCase2(TestDeterminantOp):
     def init_data(self):
         np.random.seed(0)
@@ -59,6 +67,17 @@ class TestDeterminantOpCase2(TestDeterminantOp):
         self.target = np.linalg.det(self.case)
 
 
+class TestDeterminantOpCase2FP16(TestDeterminantOp):
+    def init_data(self):
+        np.random.seed(0)
+        # not invertible matrix
+        self.case = np.ones([4, 2, 4, 4]).astype(np.float16)
+        self.inputs = {'Input': self.case}
+        self.target = np.linalg.det(self.case.astype(np.float32)).astype(
+            np.float16
+        )
+
+
 class TestDeterminantAPI(unittest.TestCase):
     def setUp(self):
         np.random.seed(0)
diff --git a/python/paddle/tensor/linalg.py b/python/paddle/tensor/linalg.py
index 3dcbc7c6ac63b26d6d63f09e13a2dff24f29bfe5..2235cf93cfb60d9693f35a19aeb7dc98db71763e 100644
--- a/python/paddle/tensor/linalg.py
+++ b/python/paddle/tensor/linalg.py
@@ -1809,7 +1809,7 @@ def det(x, name=None):
     if in_dygraph_mode():
         return _C_ops.det(x)
     else:
-        check_dtype(x.dtype, 'Input', ['float32', 'float64'], 'det')
+        check_dtype(x.dtype, 'Input', ['float16', 'float32', 'float64'], 'det')
 
         input_shape = list(x.shape)
         assert len(input_shape) >= 2, (