A numerical study is conducted to investigate the Richtmyer-Meshkov instability (RMI) of a V-shaped interface accelerated by a shock wave under various initial amplitude and shock intensity conditions. RMI on a single-mode interface is also simulated for comparison. The results show that the mixing width of a V-shaped interface generally develops faster than that of the single-mode one, which should be attributed to the fact that all initial higher-order modes of V-shaped interface have the same sign. Subsequently, comparative analyses between simulations and various theoretical models are performed. For RMI with small initial amplitude, the YZS linear model, which takes into account the influence of compressibility more comprehensively, better normalizes the mixing width in the linear growth stage than the impulsive linear model. The predictions of the ZS model, which considers the effect of mode self-coupling, are in good agreement with the results of simulations in nonlinear growth stage. For RMI with high initial amplitude, the theoretical models considered fail to predict the results of the calculation. Finally, the amplitude growth of each mode obtained through Fourier analysis is compared with predictions of different linear models. It is found that the YZS model still provides a better prediction of the numerical results than the impulsive model in the linear stage.