In pedestrian-dense traffic scenarios, an autonomous vehicle may have to safely drive through a crowd of pedestrians while the vehicle tries to keep the desired speed as much as possible. This requires a model that can predict the motion of crowd pedestrians and a method for the vehicle to predictively adjust its speed. In this study, the model-based predictive control (MPC) was combined with a social-force based vehicle-crowd interaction (VCI) model to regulate the longitudinal speed of the autonomous vehicle. The predictive feature of the VCI model can be precisely utilized by the MPC. A criterion for simultaneously guaranteeing pedestrian safety and keeping the desired speed was designed, and consequently, the MPC was formulated as a standard quadratic programming (QP) problem, which can be easily solved by standard QP toolbox. The proposed approach was compared with the traditional proportional-integral-derivative (PID) control approach for regulating longitudinal speed. Scenarios of different pedestrian density were evaluated in simulation. The results demonstrated the merits of the proposed method to address this type of problem. It also shows the potential of extending the method to address more complex vehicle-pedestrian interaction situations.