diff --git a/src/ops/conv1d_gpu.cu b/src/ops/conv1d_gpu.cu
index 6f4d10b39..11ba48a1f 100644
--- a/src/ops/conv1d_gpu.cu
+++ b/src/ops/conv1d_gpu.cu
@@ -28,6 +28,7 @@ namespace ctranslate2 {
       const int input_length = input.dim(2);
       const int output_length = output.dim(2);
       const int out_channels = weight.dim(0);
+      const int in_channels_per_group = weight.dim(1);
       const int kernel_size = weight.dim(2);
 
       cudnnDataType_t data_type = cuda::get_cudnn_data_type(input.dtype());
@@ -45,7 +46,7 @@ namespace ctranslate2 {
       cudnnFilterDescriptor_t weight_desc;
       CUDNN_CHECK(cudnnCreateFilterDescriptor(&weight_desc));
       CUDNN_CHECK(cudnnSetFilter4dDescriptor(weight_desc, data_type, CUDNN_TENSOR_NCHW,
-                                             out_channels, in_channels, 1, kernel_size));
+                                             out_channels, in_channels_per_group, 1, kernel_size));
 
       cudnnConvolutionDescriptor_t conv_desc;
       CUDNN_CHECK(cudnnCreateConvolutionDescriptor(&conv_desc));
@@ -57,6 +58,8 @@ namespace ctranslate2 {
                                                   CUDNN_DATA_FLOAT));
 
       CUDNN_CHECK(cudnnSetConvolutionMathType(conv_desc, CUDNN_DEFAULT_MATH));
+      if (_groups > 1)
+        CUDNN_CHECK(cudnnSetConvolutionGroupCount(conv_desc, _groups));
       if (data_type == CUDNN_DATA_HALF)
         CUDNN_CHECK(cudnnSetConvolutionMathType(conv_desc, CUDNN_TENSOR_OP_MATH));
 
diff --git a/tests/ops_test.cc b/tests/ops_test.cc
index 8c18fd6da..7d7b376fa 100644
--- a/tests/ops_test.cc
+++ b/tests/ops_test.cc
@@ -1105,8 +1105,6 @@ TEST_P(OpDeviceFPTest, Conv1DPaddingAndStride) {
 
 TEST_P(OpDeviceFPTest, Conv1DGroupNoBias) {
     const Device device = GetParam().device;
-    if (device != Device::CPU)
-        GTEST_SKIP() << "Grouped convolution is not implemented for CUDA.";
     const DataType dtype = GetParam().dtype;
     const float error = GetParam().error;
     const StorageView expected({2, 2, 2}, std::vector<float>{
@@ -1136,7 +1134,7 @@ TEST_P(OpDeviceFPTest, Conv1DGroupNoBiasQuantized) {
 #endif
     const Device device = GetParam().device;
     if (device != Device::CPU)
-        GTEST_SKIP() << "Grouped convolution is not implemented for CUDA.";
+        GTEST_SKIP() << "Grouped quantized convolution is not implemented for CUDA.";
     const DataType dtype = GetParam().dtype;
     const float error = std::max(GetParam().error, float(3e-3));
     const StorageView expected({2, 2, 2}, std::vector<float>{
@@ -1166,8 +1164,6 @@ TEST_P(OpDeviceFPTest, Conv1DGroupNoBiasQuantized) {
 
 TEST_P(OpDeviceFPTest, Conv1DGroup) {
     const Device device = GetParam().device;
-    if (device != Device::CPU)
-        GTEST_SKIP() << "Grouped convolution is not implemented for CUDA.";
     const DataType dtype = GetParam().dtype;
     const float error = GetParam().error;
     const StorageView expected({2, 2, 2}, std::vector<float>{