diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index f5a6a751acfd5..d6be18183021f 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -1957,8 +1957,15 @@ static void ggml_cuda_mul_mat_batched_cublas_impl(ggml_backend_cuda_context & ct
 
         size_t src1_stride_size = sizeof(cuda_t);
 
-        dim3 block_dims(ne13, ne12);
-        k_compute_batched_ptrs<<<1, block_dims, 0, main_stream>>>(
+        const int threads_x = 16;
+        const int threads_y = 16;
+        dim3 block_dims(threads_x, threads_y);
+
+        dim3 grid_dims(
+            (ne13 + threads_x - 1) / threads_x,
+            (ne12 + threads_y - 1) / threads_y
+        );
+        k_compute_batched_ptrs<<<grid_dims, block_dims, 0, main_stream>>>(
                 src0_ptr, src1_ptr, dst_t,
                 ptrs_src.get(), ptrs_dst.get(),
                 ne12, ne13,
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 991c62597962d..be1ed7cf29ba3 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -6562,6 +6562,9 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
             test_cases.emplace_back(new test_mul_mat(type_a, type_b, 16,  1, 1024, {3, 2}, {1, 1}));
             test_cases.emplace_back(new test_mul_mat(type_a, type_b, 16,  8, 1024, {3, 2}, {1, 1}));
             test_cases.emplace_back(new test_mul_mat(type_a, type_b, 16, 16, 1024, {3, 2}, {1, 1}));
+
+            // test cases with large batch size
+            test_cases.emplace_back(new test_mul_mat(type_a, type_b, 16, 8, 256, {1536, 1}, {1, 1}));
         }
     }
     for (ggml_type type_a : other_types) {