Abstract: The traditional method to overcome the instability of numerical shock is to increase the viscosity of numerical schemes, which in turn brings great challenges to the simulation of multi-media problems requiring clear identification of material interfaces.In order to overcome the numerical instability of HLLC approximate Riemann solver in the calculation of strong shock problems, the mechanism and key factors causing the numerical shock instability are studied. The role of the numerical flux component in the development of shock wave instability is analyzed by low Mach asymptotic analysis. The main reasons for the instability of HLLCM method are found. Based on this, a simple, low dissipation and contact-preserving stable scheme is proposed. The effectiveness and robustness of the proposed method are verified by numerical experiments.