This paper addresses the fuel-optimal control problem of satellite relative orbit transfer on an arbitrary elliptical orbit based on Legendre pseudospectral method.Firstly,the relative motion equations are formulated with the true anomaly as the independent variable,which are much simple.To ensure the consistency with the dynamic equations,a special cost function is proposed.Next,the optimal control problem is transformed to a parameter optimization problem using Legendre pseudospectral method.Based on the state translation matrix,a control law is obtained under the constraint of the start and final state.Then,to the linear model,another control law based on the whole state equation is presented.Unlike the methods in the literature,the above control laws are both analytical,and no computer soft is needed.Finally,the numerical results show that the control laws work well for the fuel-optimal relative orbit transfer.