In this paper, the theoretical insight into Gaussian approximation of channel capacity for several classes of Rayleighfading multiple-antenna systems is presented. In particular, a theorem, which has not been developed by the former studies of Gaussian approximation, is introduced to these systems. Then guided by this theorem, a new approach of determining the approximate mean and variance for Gaussian approximation is proposed, which is simpler and more intuitive than the existed approach. The simulation results show the availability of such new approach.