diff --git a/source/module_basis/module_ao/test/CMakeLists.txt b/source/module_basis/module_ao/test/CMakeLists.txt
index 8234a45c21e..0e37619147e 100644
--- a/source/module_basis/module_ao/test/CMakeLists.txt
+++ b/source/module_basis/module_ao/test/CMakeLists.txt
@@ -114,6 +114,13 @@ AddTest(
     LIBS ${math_libs} device base
 )
 
+install(FILES parallel_2d_test.sh DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
+find_program(BASH bash)
+add_test(NAME parallel_2d_test_para4
+      COMMAND ${BASH} parallel_2d_test.sh
+      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+)
+
 AddTest(
     TARGET parallel_orbitals_test
     SOURCES parallel_orbitals_test.cpp ../parallel_2d.cpp ../parallel_orbitals.cpp
diff --git a/source/module_basis/module_ao/test/parallel_2d_test.cpp b/source/module_basis/module_ao/test/parallel_2d_test.cpp
index eb8a836cb76..df386e6da57 100644
--- a/source/module_basis/module_ao/test/parallel_2d_test.cpp
+++ b/source/module_basis/module_ao/test/parallel_2d_test.cpp
@@ -175,12 +175,18 @@ TEST_F(test_para2d, Serial)
         //1. set dim0 and dim1
         p2d.set_proc_dim(1);
         EXPECT_EQ(p2d.dim0 * p2d.dim1, 1);
+        EXPECT_EQ(p2d.dim0, 1);
+        EXPECT_EQ(p2d.dim1, 1);
 
         //2. set_serial
         p2d.set_serial(gr, gc);
         EXPECT_EQ(p2d.get_row_size(), gr);
         EXPECT_EQ(p2d.get_col_size(), gc);
         EXPECT_EQ(p2d.get_local_size(), gr * gc);
+        for (int i = 0; i < gr; ++i)
+            EXPECT_EQ(p2d.local2global_row(i), i);
+        for (int i = 0; i < gc; ++i)
+            EXPECT_EQ(p2d.local2global_col(i), i);
 
         //3. set_global2local
         p2d.set_global2local(gr, gc, false, ofs_running);
diff --git a/source/module_basis/module_ao/test/parallel_2d_test.sh b/source/module_basis/module_ao/test/parallel_2d_test.sh
new file mode 100755
index 00000000000..94c60d40009
--- /dev/null
+++ b/source/module_basis/module_ao/test/parallel_2d_test.sh
@@ -0,0 +1,13 @@
+#!/bin/bash -e
+
+np=`cat /proc/cpuinfo | grep "cpu cores" | uniq| awk '{print $NF}'`
+echo "nprocs in this machine is $np"
+
+for i in 2 3 4; do
+    if [[ $i -gt $np ]];then
+        continue
+    fi
+    echo "TEST in parallel, nprocs=$i"
+    mpirun -np $i ./parallel_2d_test
+    break    
+done