Abstract: Here, a meteorological traditional global pseudo-spectral scheme of barotropic primitive equation is restructed and a corresponding perfect energy conservative new scheme is formufated in accordance with the compensation principle of discrete computation. Thus, the problems of both nonlinear computational instability and perfect energy conservation are completely solved, and the computational function of the traditional scheme is improved. As the numerical experiments of the new schemes show, by solving the problem of energy conservation, the new shceme in computational practice can solve their own problem of(nonlinear) computational instability and that of(nonlinear) computational convergence under certain condition. Further contrasts between the new schemes and the traditional one also indicate that, in discrete computational practice the new scheme in case of nondivergence is capable of enlarging the valid integral time of the corresponding traditional scheme, capable of solving its own problem of "climate drift",while at the same time improving its computational accuracy and reducing its amount of computation. The working principle of this paper can also applied in the case of baroclinic primitive equation.