Abstract: The Richtmyer-Meshkov (RM) instability induced by converging shock waves at interfaces of different substances has an important academic significance and engineering background in the field of inertial confinement fusion. The macroscopic fluid dynamics method based on grid discretization requires high order precision algorithm to track the interface evolution accurately because of numerical diffusion problem, and it is extremely difficult to track the complex interface evolution such as large deformation and fragmentation merging, etc. Smoothed particle hydrodynamics (SPH) method is a pure Lagrangian algorithm, which can effectively overcome the addressed difficulties. However, the classical SPH algorithm requires artificial viscosity to smooth the strong discontinuities, otherwise large non-physical oscillations may occur. For the problem involving strong shock instability, it is difficult to achieve ideal results. In this paper, the SPH algorithm based on HLL Riemann solver is adopted to effectively distinguish and track the strong shock wave and the material interface with a large density ratio. The reliability and robustness of the code were validated by four classical 1D shock tube tests, and it is found that the smoothing effect of the density algorithm used by SPH on the contact discontinuity can be improved by reducing the initial particle spacing. The smaller the initial particle spacing, the higher the numerical simulation accuracy, but it cannot be completely eliminated. However, the position of the interface is actually marked by the media properties of the particles, and does not affect the discrimination of the interface position under the SPH Lagrangian algorithm. Then the 2D cases of RM instability induced by cylindrical converging shock wave impacting at the quadrilateral light/heavy gas interface were simulated. It is found that the simulation results are quantitatively in good agreement with the existing experimental results. By analyzing the density and pressure changes in the process of interface evolution, it is also found that the models and methods adopted can accurately track the complex interfaces and shock waves evolution patterns during the RM instability process. The relevant results lay a foundation for further understanding and explanation of RM instability mechanism under extreme converging shock conditions.