A pedestrian’s active obstacle avoidance behavior has an important impact on crowd safety in heterogeneous crowd movements, but how it affects the movement of individuals and crowd is not yet clear. This study proposes a detour anisotropic social force model (DASFM) that considers active obstacle avoidance behavior for future collision prediction. DASFM prioritizes moving obstacle pedestrians based on velocity obstacle (VO) and combines the anisotropic social force model (ASFM) to achieve the dynamic process of pedestrian active obstacle avoidance behavior. The results show that DASFM enables individuals to safely overtake while avoiding fluctuations in pedestrian speed and distance between pedestrians. The model improved abnormal “strip group” crowd aggregation, individual jostling, and congestion found in other models. It has effective performance in spatial distribution, trajectory, density evolution, and time consumption of crowd movement in unidirectional flow under open conditions. The fundamental diagram generated by DASFM in unidirectional flow under periodic boundary conditions tends to be consistent with the observations and experimental results of other researchers. Instantaneous flow analysis shows that overtaking behavior alleviates local congestion in the low-density crowd and promotes the slow flow of the high-density crowd. However, overtaking behavior also exacerbates the stop-and-go waves of the high-density crowd, posing a threat to crowd safety. This study not only effectively realizes the simulation of overtaking behavior among individuals and crowds, but also discovers the impact patterns of overtaking behavior on low- or high-density crowd. Therefore, measures should be taken to control individual overtaking behavior in high-density crowd to prevent the production of stop-and-go waves.