Abstract: A completely new meshless method for the numerical simulation of the shock-induced combustion is developed in this paper. The two-dimensional Euler equations are employed. The spatial derivatives are approximated by using a local least-squares curve fitting based on clouds. The inviscid flux is calculated by a multi-component HLLC scheme. The four-stage Runge-Kutta algorithm is used to advance the integration in time. The chemical kinetics is modeled using a finite rate reaction model. The flow fields of the shock-induced combustion in different mixtures are simulated for validation. The results agree well with the numerical results of mesh-based methods, which indicates that the method is reliable in the numerical simulation of flow fields of shock-induced combustion.