Using the fixed point theorem and the integral equation

we established the sufficient condition of the existence and uniqueness of solution to the nonlinear third-order three-point boundary value problem with p-Laplacian operator.The problem was equivalent to the existence and uniqueness of fixed point of an integral operator

and then the sufficient condition of existence and uniqueness of solution to the problem was given on the basis of the Banach fixed point theorem.Thus our results make a theoretical foundation for the further study of the boundary value problem with p-laplacian operator.