Purpose: The purpose of this study is to develop the statistical test for process capability index $C_p$ based on mixture normal process. Methods: This study uses Bootstrap method to calculate the approximate P-value for various simulation conditions under mixture normal process. Results: This study indicates that our proposed method is effective way to test for process capability index $C_p$ based on mixture normal process. Conclusion: This study finds out that statistical test for process capability index $C_p$ based on mixture normal process is useful for real application.