Abstract: The Richtmyer-Meshkov (RM) instability of the premixed flame interface is common in natural phenomena and engineering applications. The current researches on the reactive RM instability mainly focus on the situation of homogeneous medium. However, the real premixed gas is usually inhomogeneous. Therefore, it is necessary to study the flame interface evolutions and the mixing characteristics in the inhomogeneous medium. The present study adopted the Navier-Stokes equations with a single-step reaction and the computational scheme with high resolutions to numerically research the RM instability induced by an incident shock wave and its reflected shock wave. The effects of chemical reactivity and inhomogeneity on the development and the mixing characteristics of flame interface were investigated. The results show that during the stage after the passage of incident shock wave, the flame interface morphology presents the typical "spike-cap-bubble" structures in homogeneous medium, and the more reactive the premixed gases, the rapider the growth for both "spike" and "bubble" structures. While in inhomogeneous premixed gases, the flame interface morphology presents the "spike-spike" structures, and the interface is stretched much more significantly due to the difference of flow velocity. The results also show that during the stage after the passage of first reflected shock wave, the growth of the mixing zone does not depend on the chemical reactivity and inhomogeneity, but only on the flow characteristics. The analysis of time-scales shows that the large-scale flow dominates development of the reactive RM instability, followed by chemical reaction and small-scale mixing. The intensification of chemical reaction inhibits the large-scale flow, and the inhomogeneity strengthens the large-scale flow.