Based on the treatment that the rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, an approximate method for calculating the generalized beam propagation factor (M2-factor) is proposed. A truncated flattened Gaussian beam (FGB) and a truncated cosh-Gaussian beam (CGB) are taken as two examples of truncated laser beams. The analytical expressions for the generalized M2-factor are derived. The typical numerical examples are given and compared to those obtained from numerical integration and the known analytical method. A comparison of the results for the ideal beam models with the more realistic ones is discussed.