Platoon of connected autonomous vehicles has the potential to increase traffic flow while also alleviating congestion. However, there are several challenging problems with heterogeneous connected autonomous vehicles control currently. Platoons with heterogeneous vehicles are especially susceptible to the negative effects of wireless communication. A multi-objective heterogeneous asymmetric sliding mode control strategy is proposed in this paper to solve this problem. In this paper, a nonlinear vehicle dynamic model is considered. Then, a sliding mode controller is designed to achieve consensus. Moreover, Riccati inequality and Lyapunov analysis are used to find the controller's gains and guarantee Lyapunov stability and string stability with the linear matrix inequalities. Finally, a non-dominated sorting genetic algorithm II is utilized to find the Pareto optimal heterogeneous asymmetric degrees regarding the overall performance of the platoon, including tracking index, fuel consumption and acceleration standard deviation. The results show that the proposed strategy can effectively deal with platoons of heterogeneous vehicles while ensuring stability. At the same time, Pareto optimal heterogeneous asymmetric degrees can be obtained for each vehicle in the platoon. The proposed method improves platoon's tracking ability by 76.2%, fuel economy by 3.53% and driving comfort by 3.52%.