A numerical scheme for integrating the primitive equation over the spherical earth with a quasi-uniform grid system, which is an icosahedral-hexagonal grid, is presented. Making use of the stream function and the velocity potential, all the components of the primitive equations are expressed by Jacobian, Laplacian and flux divergence terms. The finite difference forms for these terms are represented by the line-integral which is easy to form mass a conserving scheme. The scheme presented here conserves exactly the totaland almost exactly the total energy and absolute potential enstrophy of a simple divergent flow. 100 days forecast was performed by this grid system with the Rossby-Haurwitz wave as the initial condition. The total mass was conserved satisfactorily, and the conservation of total energy was also achieved within 0.001% error throughout 100 days integration. The error in the conservation of total absolute potential enstrophy is 0.01-0.1%, and the results of 100 days forecast are satisfactory.