The beam propagation M2 factor is a useful parameter for characterizing laser beam. By using the treatment that the rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, approximate formulas for the second-order moments of partially coherent beam after it passes hard-edge diaphragm are given. The generalized M2 factor of partially coherent beam after it passes hard-edge diaphragm can be obtained. A laser beam with amplitude modulation and phase distortion is taken as a typical example of partially coherent beams. The analytical expression for the generalized M2 factor is derived. The calculation precision of our method is analyzed by numerical calculations. It can been seen from the study that by making use of the approximate calculation method proposed, the calculation error for the generalized M2 factor is less than 1% and the approximate analytic expressions can be obtained immediately. Consequently, the calculation can be simplified and the calculation efficiency can be improved efficiently.