In this paper, a new efficient performance evaluation method is suggested and its efficiency is verified in terms of computer simulation time for QPSK satellite channel. Importance Sampling technique aimed for minimizing the overall computational burden is known to be difficult to implement for QPSK channel. However, in order to solve the difficulties of the existing Importance Sampling techniques, we adopted the discrete probability mass function in the new method for estimating the statistical characteristics of received signals from the measured central moments up to $N_th orders. From the discrete probability mass function constructed with the measured central moments with less number of the received signal samples than the one required in the MC technique, continuous cumulative probability distribution function can be exactly estimated by using interpolation and extrapolation technique. By assuming that the in-phase and quadrature phase received signals are independent and by estimating the channel characteristics of the in-phase and quadrature phase received signals separately, the implementation of the proposed method could be simplified. With the simplified channel performance evaluation model, the overall channel performance evaluation can be done within a drastically reduced time. The simulation results applied to the nonlinear digital satellite QPSK channel showed the great efficiency of the proposed method in the sense of computer run time, and demonstrated that the existing problems of IS for the QPSK nonlinear satellite channels.