Kinematic control for continuum robots usually involves an inverse model to provide actuator positions according to the desired end-tip position, as well as a servo controller at the actuator level. The resulting control performance of a continuum robot is then related to its kinematic characteristics that vary at different configurations. In this paper, a kinematic model for a typical rod-driven continuum robot is presented. Following this, a kinematic parameter, velocity sensitivity, is proposed to evaluate the kinematic characteristics of the continuum robot, indicating the contribution of the individual actuators to the instant movement of the end-tip when tracking a given path. Next, a variable gain control strategy is presented to tune the servo controller with respect to the varying velocity sensitivity along the path, reducing the fluctuation of the tracking errors in real time. The simulated and experimental results show that the presented methods can effectively smooth the movement of the continuum robot over its workspace by considering the coordination between the kinematic and servo controllers.