Abstract: Based upon an even gridpoint difference model, a global gridpoint multilevel primitive equation difference model with variable resolution has been designed. It is shown that in the adiabatic and inviscid case, if the former model satisfies certain conditions, and can be proved to be mass-and energy-conserving, and has consistent conversions between kinetic energy, potential energy and surface potential energy in the continuous case, the latter model also has similar properties. Furthermore, it is quite convenient to transform the former model into the latter one, and the amount of extra work is small.