Abstract: Based on a modified MM4 and a limited-area variable resolution gridpoint model, a global multilevel primitive equation gridpoint model with variable resolution has been formulated. It can be proved that the model possesses the integral properties such as mass and energy conservation, and correct transformation between kinetic energy and complete potential energy. In order to overcome the difficulties caused by the fact that the time step chosen should be very small due to the confluent meridians in high-latitudes, a settlement of the problem without filtering waves is suggested, with which the integral properties could be preserved.