A new distributed robust economic model predictive control(EMPC) strategy is proposed to solve the problem of distributed cooperative control of heterogeneous vehicle platoons under bounded disturbances for energy saving and stablility. Firstly, the uncertain error model is used to describe the longitudinal driving dynamic characteristics of heterogeneous vehicle platoons under bounded disturbances, and the system constraints are tightened by applying the tube idea to compensate the uncertainty of the bounded disturbances on the system. Secondly, the finite-time optimal control problem of vehicle platoon distributed economic performance optimization is described based on the local vehicle driving energy consumption model, and the additional stability shrinkage constraint function is designed by using the traditional tracking performance index. Furthermore, based on the principle of system shrinkage, the conditions about input-to-state stability of the vehicle platoon closed-loop system with respect to bounded disturbances are established. Finally, compared with the numerical simulation results of the traditional distributed robust model predictive control strategy for vehicle platoons, the effectiveness and superiority of the strategy proposed in this paper are verified.