In this paper, under some assumptions a nonlinear controller based on differential geometry theory of nonlinear control system and pole-assignment method is designed, and applied to synchronize output signals of high dimensional chaotic system. Using the method, we can synchronize output signals formed by linear or nonlinear composition of single or multiple state variables of the chaotic system. The controller is easy to be realized and can be adapted to a lot of nonlinear systems. Computer simulation results show the excellent performance of the proposed method.