Based on the method of generalized truncated second-order moment, the analytical formula of the generalized beam propagation factor (M2G factor) of truncated partially coherent Hermite-Gaussian(H-G) beams is derived. The analytical results obtained from truncated fully coherent H-G beam, truncated Gaussian Shell Model (GSM) beam and truncated Gaussian beam are given as particular examples in this paper. It is shown that the M2G factor of truncated partially coherent H-G beam depends on truncated parameter δ, beam order m, and beam coherence parameter α. When the value of δ is very small, the odd-even groups happen to the M2G factor, i.e., the values of M2G factor with different values of the odd m are nearly the same, and so are they for the even m case. However, this phenomenon disappears as δ increases. For the truncated GSM beams with different values of δ, there exist the cross points between the curves of the M2G factor versus α. However, this phenomenon may disappear for truncated partially coherent H-G beams. In addition, the larger the m is, the more the M2G factor is affected by the δ, and the effect of aperture on M2G factor may be neglected when the δ is larger.