In this paper, a new fuzzy sliding mode control algorithm is presented for trajectory control of robot manipulators. A fuzzy logic is applied to a sliding mode control algorithm to have the sliding mode gain adjusted continuously through fuzzy logic rules. With this scheme, te stability and the robustness of the proposed fuzzy logic control algorithm are proved and ensured by the sliding mode control law. The fuzzy logic controller requires only a few tuning parameters to adjust. Computer simulation results are given to show that the proposed algorithm can handle uncertain systems with large parameter uncertainties and external disturbances.