In this paper, a prescribed performance controller is proposed for robotic systems with unknown system dynamics and external disturbances, where the widely-used function approximation can be avoided, and both the transient and steady-state performances can be retained. The unknown system dynamics (e.g., coriolis/centripetal force, gravity torque) and external disturbances are estimated simultaneously via an unknown system dynamics estimator. The salient feature of the estimator over other schemes is that its structure is simple and only one parameter needs to be tuned. Moreover, the joint accelerations are avoided by introducing filter operations, making the estimator suitable for practical robotic control application. By employing a performance function that characterizes the convergence rate, maximum overshoot and steady-state error, the tracking error of the robotic system can be retained within a prescribed bound. The stability of the closed-loop control system is proved via Lyapunov theory. Simulations and experiments are carried out to validate the effectiveness of the proposed schemes.