Abstract: Two-dimensional simulations of Richtmyer-Meshkov (RM) instability of small-amplitude initial perturbed interface induced by shock waves are performed by using Navier-Stokes equations. The evolution of interface mixing zone, which is considered as a combination of a bubble and a spike before and after the passages of reshock wave, is analyzed under the single-mode and random multi-mode initial perturbed conditions. The results show that the perturbation growth is influenced by the initial patterns of interface before and after the passages of reshock wave. The information of initial perturbed interface pattern can be transmitted to that of the interface after reshock wave by transforming between the bubble and spike. The growth rate of spike on the interface dominates the whole growth rate of the mixing zone. The developed spike with crown shape before the passage of reshock is transformed into the complex bubble structure that drags the development of spike after the passage of reshock wave. The evolution of random multi-mode perturbed interface shows the similar behavior as that of single-mode perturbed interface. However, the asymmetric feature of complex bubble structure on random multi-mode interface weakens the drag effect on the development of spike, and thus gives rise to the faster growth of the random multi-mode interface than that of the single-mode interface, under the conditions of similar initial wave length for both interfaces.