Abstract: The non-standard Richtmyer-Meshkov instability is numerically realized and theoretically analyzed on a planar heavy/light(Kr/N₂) gas interface subjected to two successive shocks within a Mach reflection(MR) wave configuration. The incident MR wave configuration is generated by diffracting a planar shock over a rigid cylinder, and an initial planar interface is considered. Results indicate that the first impact of the leading shock front undergoes regular refraction with a reflected expansion, subsequently, the transverse reflected second impact within the MR wave configuration experiences bound precursor refraction. After these two successive impacts, the interface is divided into three distinct segments, which exhibit different evolving processes in each segment. Furthermore, a three-step analytical method based on three shock theory is developed. The corresponding theoretical solution is compared with the numerical results, which demonstrates the theoretical method can accurately predict the post-shock wave angle, interface deflection angle, velocity perturbation and circulation deposition. Quantitative results reveal that the successive shock process plays a dominant role in modulating the instability evolution. Specifically, the second impact makes significant negative contribution to both velocity perturbation and circulation deposition induced by the first impact. These findings reveal that the second shock within the MR wave configuration remarkably suppresses the growth of the interface instability.