Abstract: Growth of mixing zone on premixed flame interface induced by Richtmyer-Meshkov (RM) instability occurs frequently in natural phenomena and in engineering applications. The effect of chemical reaction on the growth mechanism of mixing zone on the interface still remains unknown, and the predictions on growth rate of mixing zone on reactive interface were seldom reported. Therefore, it is necessary to study the interface evolutions and the predictions of mixing zone on the premixed flame interface during the RM instability. 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 of flame interface with sinusoidal pattern, induced by a planar incident shock wave and its reflected shock wave. The results in present study show that during the stage after the passage of incident shock wave, besides the RM instability mechanism which leads to the "spike-cap" and "bubble" structures of the interface, the chemical reaction not only promotes the "bubble" structure growth in the form the premixed flame propagation, but also gives rise to the growth of "spike-cap" structure through the interaction with vortices structure. The more reactive the premixed gases, the rapider the growth for both "spike-cap" and "bubble" structures. The results also show that during the stage after the passage of first reflected shock wave, the chemical reaction has the same effects on the developments of both "spike-cap" and "bubble" structures in the mode of premixed flame propagation. The counteraction between both effects results in the independence of mixing zone growth on the chemical reaction. Based on above analyses, the predicted models for the stages after passages of incident shock wave and reflected shock wave are proposed, respectively, in order to provide a useful method for predictions of mixing zone growth during the reactive RM instability.