This paper addresses the keeping control problem of the leader-follower satellite formation by using an economic model predictive control method. The objective function in the designed economic model predictive control is comprised of two parts. One part is an adjustment term which is used to realize the trajectory tracking. The other part is an economic term l_e which achieves fuel optimization. In addition, genetic algorithm is used to solve the control law which realizes the keeping control of satellite formation. Simulation results show that the proposed control method can achieve fuel optimization control for satellite formation.