A method for the generalized M2 factor measurement and the corresponding data processing have been proposed, which can be widely applied to the truncated and non-truncated laser beams. The integral area for calculating the beam width by using the definition of generalized second-order moments is selected to ensure the energy in the angular domain more than 75% of the total beam energy and the measurement method and steps still follow the relevant ISO standards. The generalized M2 factor of truncated Gaussian beam has been measured. The experimental results for different truncated parameters have been compared with the theoretical results, showing the validness of the method proposed. The results indicate that the generalized M2 factor of truncated laser beam can be measured only by properly modifying the data processing method for the measurement of M2 factor of non-truncated laser beam without additional hardware spending. The method is simple and convenient and its measuring steps also follow the ISO standards.