In order to evaluate the wave-induced mixing in the upper ocean and the impact of surface waves on ocean-atmosphere fluxes, a global wave numerical model in spherical coordinates is developed based on the previous LAGFD-WAM regional model. The wave energy spectrum balance equation and its complicated characteristic equations are derived in spherical coordinates. In these control equations, the modulation of background current to wave evolution and the refraction of waves propagating along great circles are included. The characteristic inlaid method is applied to integrating the wave energy spectrum balance equation. Primary calibration indicates that the global wave model can describe the dynamical processes of ocean surface gravity waves.