We study the budget allocation problem in continuous scenario-based simulation optimization. Due to the constraint that multiple observations at every scenario and decision are unavailable, the original theory may fail to provide an estimation on the probability of falsely identifying the optimal decision, which enables allocating budget optimally. In this study, we incorporate a surrogate method to estimate this probability in the homoscedastic setting and propose a new adaptive budget allocation. Numerical experiments are conducted and show that our method improves the probability of correct identification significantly.