As a new type of bionic manipulator, the continuum manipulator has a good potential application prospect. This paper tackles the issue of trajectory tracking control for a continuum manipulator possessing two degrees of freedom (DOF). Given that the accuracy of tracking control system designed based on nominal model is commonly affected by modeling errors, external frictions and parameter perturbations. We develop a fuzzy PID control strategy to design the tracking controllers for the manipulator. This control strategy first design PID tracking controllers using the tracking error information. And then, the fuzzy logic technique is utilized to adjust the PID controller parameters adaptively. This enables the continuum manipulator to quickly track the desired motion trajectory. The numerical simulations show the validity of the presented method.