We present a model of overtaking behavior that can be used to simulate unidirectional pedestrian flow in routine. All pedestrians have the ability to determine whether or not to overtake other pedestrians according to their desired velocity and position. Although existing models such as cellular automata models, lattice gas models, social force models, etc., can be used to predict evacuation performance, most of these models are either computationally inefficient or do not account for some crucial elements of human behavior in a moving crowd. Furthermore, these models use either empirical equations developed from experiments or mechanical system analogies to determine movement decisions. The pedestrian flow patterns simulated by these models may deviate significantly from reality. In reality, pedestrians walk at different velocities and pedestrians with a higher walking velocity are accustomed to overtaking other pedestrians with a lower walking velocity and this paper aims to mimic this behavior as the original social force model developed by Helbing et al. does not reflect this pattern of collective pedestrian behavior. In this paper, we propose modifications of the social force model that reflects how overtaking behavior operates in routine. The comparison of the pedestrian flow pattern between the original social force model and the modified social force models with the real data collected by the camcorder is also performed in order to demonstrate our modified social force model can be used to achieve reasonable simulations of overtaking behavior among pedestrians.