This article develops a distributed tube model predictive control method to guarantee the string stability of the heterogeneous vehicle platoon under external disturbance and controller saturation. The error model of each vehicle is proposed based on the desired distance and velocity, where the coupled factor between vehicles is treated as a random disturbance. The linear feedback controller is devised to reject disturbances by keeping the actual trajectory within a tube around the nominal trajectory, and a model predictive controller is proposed by treating the input saturation and string stability as state constraints in the optimization problem. Compared with previous results, the proposed control strategy achieves a better performance of disturbance rejection and greatly reduces the online computation burden, which would be more favorable in engineering applications. The method proposed in this article is illustrated to be effective by simulation.