Based on extend equal area criterion（EEAC），the numerical probabilistic characteristics of the driving power of generators in a power system are first transformed into those of two coherent generator groups corresponding to the instability mode，and then the numerical probabilistic characteristics of the system stability margin are calculated via semi-invariant by using the linearized expression of stability margin，i.e.，a Taylor series with two generator groupsdriving power as variables and sensitivity parameters of the stability margin as coefficients.Therefore，the probability distribution of the transient stability margin can be calculated using the Gram-Charlier series.For the ideal two-coherent-group instability mode，fast calculation can be achieved just by an analytical method.For the nonideal two-coherent-group instability mode，sensitivity coefficients of the stability margin are calculated by time-domain simulation and a piecewise function based method is used to describe the stability margin distribution in case of sudden changes of the stability margin or sensitivity coefficients due to changes of the instability mode.The effectiveness of the proposed algorithm is verified by two numerical examples.