The more bandwidth efficient modulation schemes are used for high speed data transmission systems in the satellite communication. But these schemes are sensitive to the nonlinearity of high power amplifiers (HPA). The nonlinearity of HPA causes inter symbol interference (ISI) and adjacent channel interference (ACI). A scheme for adaptive digital predistortion based on RBF neural network for HPA onboard the satellites was proposed to linearization HPA . And the adaptive arithmetic of stochastic gradient method was derived. Simulation results show that the scheme can not only correct the constellation distortion obviously, but also improve the system BER performance greatly.