Abstract: From differential game point of view,a optimum intercept guidance law with uncertain factors is discussed on minimum-maximum principle.The target-missile relative motion equations are described as follows:where τ is time constant of missile,a（t）is proper acceleration,u（t）is control command of missile,Δa（t）is uncertain factor.If a maneuvering acceleration of target exists,it is also included in Δa（t）.The direction of Δa（t）is arbitrary,but the magnitude of Δa（t）satisfieshere ε is positive real constant.Generally speaking,the optimum intercept guidance law proposed in this paper is provided in synthetical form,i.e.it is a closed loop guidance law.When T-t0 is set specifically,the optimum intercept guidance law consists of two parts: the first part is variable coefficient proportion navigation,the other is correction term related to the acceleration of the guided missile aD0 There is a switch function x（t0,τ,T,μ,aD0）which is included in navigation coefficient and correction term respectively.