In the literature of structural break tests, it is well known that the sup-Wald test has large size distortion when the errors are serially correlated. In this paper we propose a bias-corrected sup-Wald test for a shift in mean by modifying the bias of the denominator up to O(1/T), where the long-run variance is estimated by the prewhitening method based on Andrews and Monahan (1992). Simulation results show that the proposed test has good size and high power.