This study considers the problem of testing for a parameter change in the presence of outliers. For this, we propose a robust test using the objective function of minimum density power divergence estimator (MDPDE) by Basu et al. (Biometrika, 1998), and then derive its limiting null distribution. Our test procedure can be naturally extended to any parametric model to which MDPDE can be applied. To illustrate this, we apply our test procedure to GARCH models. We demonstrate the validity and robustness of the proposed test through a simulation study. In a real data application to the Hang Seng index, our test locates some change-points that are not detected by the previous tests such as the score test and the residual-based CUSUM test.