Digital satellite communication channels have nonlinearities with memory due to saturation characteristics of traveling wave tube amplifier in the satellite and transmitter/receiver linear filters. In this paper, we propose a network structure and a learning algorithm for complex pi-sigma network (CPSK) and exploit CPSN in the problem of equalization of nonlinear satellite channels. The proposed CPSN is a complex-valued extension of real-valued pi-sigma network that is a higher-order feedforward network with fast learning while greatly reducing network complexity by utilizing efficient form of polynomials for many input variables. The performance of the proposed CPSN is demonstrated by computer simulations on the equalization of complex-valued QPSK input symbols distorted by a nonlinear channel modeled as a Volterra series and additive noise. The results indicate that the CPSN shows good equalization performance, fast convergence, and less computations as compared to conventional higher-order models such as Volterra filters.