The Richtmyer-Meshkov instability occurs when a perturbed interface between two fluids of different densities is impulsively accelerated by a shock wave. A major issue with the Richtmyer-Meshkov instability is the nonlinear growth of the interpenetrating mixing layer and ensuring turbulent mixing. The present paper represents a numerical investigation on the nonlinear evolution of the Richtmyer-Meshkov instability excited by a high-amplitude single-mode perturbation. The work simulates the Mach 1.15 shock tube experiment of Jourdan and Houas [Phys. Rev. Lett. 95, 204502, 2005]. An asymptotic analysis is also performed to provide more direct insight. Four different cases of air/SF 6, air/CO2, air/N2, and air/He are are studied, covering a wide range of Atwood numbers of -0.77∼0.6. A mixture-type interface capturing method, which can effectively avoid numerical oscillations on the interface discontinuities, is used to simulate the multi-fluid flows. The high-resolution Piecewise-Parabolic-Method (PPM) with a multi-fluid Riemann solver is employed to solve the proposed model equations. Calculated results show good agreement with experimental data and theoretical predictions.