Abstract: In order to improve the control lag caused by long delay channel in satellite communication, a new cost function is designed with low satellite receiving power and low power control error. A cost function is proposed for satellite mobile communication system. The uplink power control algorithm introduces the ARIMA link prediction model result as one of the decision criteria in the algorithm iteration process. The advantages of the cost function over the existing cost function are analyzed, and the existence and convergence of the Nash equilibrium of the algorithm are proved. Finally, the performance is verified by simulation. Simulation results show that the algorithm has some improvement over the classical algorithm.