diff --git a/source/module_base/test/CMakeLists.txt b/source/module_base/test/CMakeLists.txt
index 9dad2d8371e..e629f219558 100644
--- a/source/module_base/test/CMakeLists.txt
+++ b/source/module_base/test/CMakeLists.txt
@@ -123,6 +123,12 @@ AddTest(
   SOURCES math_chebyshev_test.cpp ../math_chebyshev.cpp ../tool_quit.cpp ../global_variable.cpp ../timer.cpp ../global_file.cpp ../global_function.cpp ../memory.cpp
 )
 
+AddTest(
+  TARGET base_lapack_connector
+  LIBS ${math_libs}
+  SOURCES lapack_connector_test.cpp ../lapack_connector.h
+)
+
 AddTest(
   TARGET base_opt_CG
   SOURCES opt_CG_test.cpp opt_test_tools.cpp ../opt_CG.cpp ../opt_DCsrch.cpp ../global_variable.cpp ../parallel_reduce.cpp
diff --git a/source/module_base/test/lapack_connector_test.cpp b/source/module_base/test/lapack_connector_test.cpp
new file mode 100644
index 00000000000..b46cfa214b6
--- /dev/null
+++ b/source/module_base/test/lapack_connector_test.cpp
@@ -0,0 +1,154 @@
+#include "../lapack_connector.h"
+
+#include <cmath>
+#include <complex>
+#include <vector>
+
+#include "gtest/gtest.h"
+
+/************************************************
+ *  unit test of lapack_connector.h
+ ***********************************************/
+
+/**
+ * - Tested Functions:
+ *  - zhegv_
+ *   - use zhegv_ to compute the eigenvalues and eigenvectors of
+ *   - a complex Hermitian-definite generalized eigenproblem
+ */
+
+class LapackConnectorTest : public testing::Test
+{
+  protected:
+    void SetUp() override
+    {
+        // Initialize matrices A and B and the eigenvalue vector
+        // (Use appropriate values for your test case)
+        A = {
+            std::complex<double>(2.0, 0.0),
+            std::complex<double>(1.0, -1.0),
+            std::complex<double>(1.0, 1.0),
+            std::complex<double>(3.0, 0.0),
+        };
+
+        // Create a random square matrix C with complex elements
+        std::vector<std::complex<double>> C = {
+            {1.0, 2.0},
+            {3.0, 4.0},
+            {5.0, 6.0},
+            {7.0, 8.0}
+        };
+
+        // Compute the conjugate transpose of C
+        std::vector<std::complex<double>> C_conj_transpose = {
+            {C[0].real(), -C[0].imag()},
+            {C[1].real(), -C[1].imag()},
+            {C[2].real(), -C[2].imag()},
+            {C[3].real(), -C[3].imag()}
+        };
+
+        // Compute the product of C_conj_transpose and C to obtain B
+        B = {{C_conj_transpose[0] * C[0] + C_conj_transpose[1] * C[1]},
+             {C_conj_transpose[0] * C[2] + C_conj_transpose[1] * C[3]},
+             {C_conj_transpose[2] * C[0] + C_conj_transpose[3] * C[1]},
+             {C_conj_transpose[2] * C[2] + C_conj_transpose[3] * C[3]}};
+
+        n = sqrt(A.size());
+        lda = n;
+        ldb = n;
+        w.resize(n);
+
+        // Set up the parameters for zhegv_
+        itype = 1;
+        jobz = 'V';
+        uplo = 'U';
+        lwork = -1;
+        info = 0;
+
+        // Ensure that B is positive definite
+    }
+
+    int itype;
+    char jobz;
+    char uplo;
+    int n;
+    int lda;
+    int ldb;
+    int lwork;
+    int info;
+    // matrices A and B are column-major
+    std::vector<std::complex<double>> A;
+    std::vector<std::complex<double>> B;
+    std::vector<double> w;
+};
+
+// Test the zhegv_ function
+TEST_F(LapackConnectorTest, ZHEGV)
+{
+    // First, query the optimal size of the work array
+    std::complex<double> work_query;
+    double rwork_query;
+    zhegv_(&itype,
+           &jobz,
+           &uplo,
+           &n,
+           A.data(),
+           &lda,
+           B.data(),
+           &ldb,
+           w.data(),
+           &work_query,
+           &lwork,
+           &rwork_query,
+           &info);
+    lwork = static_cast<int>(work_query.real());
+    std::vector<std::complex<double>> work(lwork);
+    // std::vector<double> rwork(static_cast<int>(rwork_query));
+    // the above line is not working as rwork_query will return -nan
+    // std::vector<double> rwork(7 * lwork);
+    std::vector<double> rwork(7 * n);
+
+    // Now, call zhegv_ with the optimal work array size
+    zhegv_(&itype,
+           &jobz,
+           &uplo,
+           &n,
+           A.data(),
+           &lda,
+           B.data(),
+           &ldb,
+           w.data(),
+           work.data(),
+           &lwork,
+           rwork.data(),
+           &info);
+
+    // Check that the function completed successfully
+    ASSERT_EQ(info, 0);
+
+    // Check the computed eigenvalues and eigenvectors
+    // (Use appropriate values for your test case)
+    std::vector<double> expected_eigenvalues = {0.014371905048252809, 1.0871905949517402};
+    std::vector<std::complex<double>> expected_eigenvectors = {
+        {0.00029066041795582461, -0.042636598658647745},
+        {0.07557994526773984,    0.0                  },
+        {-0.81903769393029213,   -0.083945171943878405},
+        {0.33387897788468901,    0.0                  }
+    };
+
+    for (size_t i = 0; i < n; ++i)
+    {
+        EXPECT_NEAR(w[i], expected_eigenvalues[i], 1e-8);
+        for (size_t j = 0; j < n; ++j)
+        {
+            EXPECT_NEAR(A[i * n + j].real(), expected_eigenvectors[i * n + j].real(), 1e-8);
+            EXPECT_NEAR(A[i * n + j].imag(), expected_eigenvectors[i * n + j].imag(), 1e-8);
+        }
+    }
+}
+
+int main(int argc, char** argv)
+{
+    testing::InitGoogleTest(&argc, argv);
+    return RUN_ALL_TESTS();
+}
\ No newline at end of file