diff --git a/qa/L0_cuda_graph/test.sh b/qa/L0_cuda_graph/test.sh
index 2fc58fdcc0..9388dba77d 100644
--- a/qa/L0_cuda_graph/test.sh
+++ b/qa/L0_cuda_graph/test.sh
@@ -287,6 +287,53 @@ set -e
 kill $SERVER_PID
 wait $SERVER_PID
 
+# TrtCudaGraphTest.test_nobatch_fixed_shape
+rm -rf ${DATADIR} && mkdir -p ${DATADIR}
+cp -r /data/inferenceserver/${REPO_VERSION}/qa_model_repository/plan_nobatch_float32_float32_float32 ${DATADIR}/
+# Make sure only one version is present
+rm -rf ${DATADIR}/plan_nobatch_float32_float32_float32/2 ${DATADIR}/plan_nobatch_float32_float32_float32/3
+
+CLIENT_LOG="./nobatch_fixed_shape.client.log"
+SERVER_LOG="./nobatch_fixed_shape.inference_server.log"
+echo "optimization { cuda { graphs: true } }" >> ${DATADIR}/plan_nobatch_float32_float32_float32/config.pbtxt
+
+run_server
+if [ "$SERVER_PID" == "0" ]; then
+    echo -e "\n***\n*** Failed to start $SERVER\n***"
+    cat $SERVER_LOG
+    exit 1
+fi
+
+set +e
+python $TRT_CUDA_GRAPH_TEST TrtCudaGraphTest.test_nobatch_fixed_shape plan_nobatch>>$CLIENT_LOG 2>&1
+if [ $? -ne 0 ]; then
+    echo -e "\n***\n*** Test Failed\n***"
+    cat $CLIENT_LOG
+    RET=1
+else
+    check_test_results $TEST_RESULT_FILE 1
+    if [ $? -ne 0 ]; then
+        cat $CLIENT_LOG
+        echo -e "\n***\n*** Test Result Verification Failed\n***"
+        RET=1
+    fi
+fi
+set -e
+
+set +e
+if [ `grep -c "Context with profile default \[0\] is launching CUDA graph " $SERVER_LOG` != "1" ]; then
+    echo -e "\n***\n*** Failed. Expected only one execution with CUDA graph\n***"
+    RET=1
+fi
+
+if [ `grep -c "captured CUDA graph for" $SERVER_LOG` != "1" ]; then
+    echo -e "\n***\n*** Failed. Expected 1 CUDA graph to be captured\n***"
+    RET=1
+fi
+set -e
+
+kill $SERVER_PID
+wait $SERVER_PID
 
 if [ $RET -eq 0 ]; then
   echo -e "\n***\n*** Test Passed\n***"
diff --git a/qa/L0_cuda_graph/trt_cuda_graph_test.py b/qa/L0_cuda_graph/trt_cuda_graph_test.py
index 46f442c26e..07b744c0b1 100644
--- a/qa/L0_cuda_graph/trt_cuda_graph_test.py
+++ b/qa/L0_cuda_graph/trt_cuda_graph_test.py
@@ -36,16 +36,21 @@
 
 
 class TrtCudaGraphTest(tu.TestResultCollector):
+    MODELNAME= "plan"
 
     def setUp(self):
         self.dtype_ = np.float32
         self.dtype_str_ = "FP32"
-        self.model_name_ = 'plan'
+        self.model_name_ = self.MODELNAME
 
     def _check_infer(self, tensor_shape, batch_size=1):
         try:
+            if batch_size:
+                full_shape = (batch_size,) + tensor_shape
+            else:
+                full_shape = tensor_shape
             iu.infer_exact(self,
-                           self.model_name_, (batch_size,) + tensor_shape,
+                           self.model_name_, full_shape,
                            batch_size,
                            self.dtype_,
                            self.dtype_,
@@ -132,6 +137,11 @@ def test_range_dynamic_shape(self):
         self._check_infer((16,), 8)
         self._check_infer((30,), 4)
 
+    def test_nobatch_fixed_shape(self):
+        self._check_infer((16,), 0)
 
 if __name__ == '__main__':
+    if len(sys.argv) > 2:
+        TrtCudaGraphTest.MODELNAME = sys.argv.pop()
+
     unittest.main()