Abstract: In this paper,we study an existence and uniqueness of solution for the nonlinear complementarity problem in Banach space,produce an existence and uniqueness result of solution for the nonlinear complementarity problem associated to a strictly monotone mapping and to a convex cone in a reflexive Banach space,and produce an existence result of solution for the nonlinear complementarity problem associated to the difference of two nonlinear mapping and to a weakly locally compact closed convex cone in a reflexivc Banach space.