Car-like robots are mobile robots commonly used in manufacturing and warehousing. This kind of robot has a mechanical structure similar to that of an unmanned vehicle, but it also has characteristics that have a more significant impact on path tracking control, such as a greater magnitude of reference path curvature, a smaller range of system constraints, and a lower degree of part standardization. Among the path tracking control methods for car-like robots, model predictive control (MPC) has a tremendous advantage in dealing with system constraints. However, the existing nonlinear model predictive control (Nonlinear MPC, NMPC) has poorer real-time performance, and linear model predictive control (Linear MPC, LMPC) has poorer accuracy. So, there is an urgent need to propose a path tracking control method for car-like robots with high accuracy and real-time performance simultaneously. To this end, a feedforward MPC (FMPC) method is proposed based on LMPC without preview point and feedforward steering angle information based on the inverse kinematics model, and it is tested by joint simulation with MATLAB and Carsim. The FMPC has high accuracy, the absolute value of displacement error in all the simulation results does not exceed 0.0966m, and the absolute value of the heading error does not exceed 0.1177 rad. The accuracy of FMPC is comparable to that of NMPC under the same condition, and the errors of LMPC, feedforward control, and Stanley control are dispersed under this condition. FMPC also has a high real-time performance, and the solving time in each control period does not exceed 4.31ms. Under the same conditions, FMPC is comparable to LMPC in terms of real-time performance and can reduce the maximum value of the solving time in each control cycle by 80.68% compared to NMPC. In addition, FMPC can ensure that the control variables are within the system constraints and are less affected by positioning errors.