Control of a manipulator mounted on a random vibration base is investigated in this paper. Random vibration of the base will lead to adverse effects on the performances of the manipulator. In practice, the random vibration is bounded in amplitude, the amplitude of control forces is limited as well. To deal with control problems of such manipulators, a control method based on Implicit Lyapunov function is studied in this paper. Firstly, a given manipulator mounted a random vibration base is simplified. Then, the dynamic equations of the equivalent manipulator are derived via the Lagrange equations of the second kind, and the nonlinear term caused by the base random vibration in the manipulator dynamic equations is treated as the bounded perturbation. Finally, a controller design methodology, which is mainly based on the theory of Lyapunov stability of motion, is presented. A feedback controller, with coefficients depending upon the generalized coordinates, is constructed by an implicitly given Lyapunov function. By using MATLAB package, the numerical simulation of the above-mentioned control system is carried out. The numerical results show that the controller can steer the system to the final state in a finite time, whereas the feedback coefficients increase to infinity as the trajectory approaches the terminal state, but the control forces remain bounded and satisfy the conditions imposed on them.