Richtmyer-Meshkov Instability (RMI) in a spherical geometry is studied via direct numerical simulation using a high-order three-dimensional in-house solver. Specifically, a six-order compact difference scheme coupled with localized artificial diffusivity method is adopted in order to capture discontinuities with high accuracy. A pure converging shock propagation in a sphere is simulated and the result agrees well with Guderley's theory. For RMI in a spherical geometry, the development of mixing width and its growth rate at different stages are examined and the underlying mechanism is also briefly analyzed. Particularly addressed is the effect of Mach number on the growth rate of perturbations and turbulent mixing process.