Similar to the traditional adaptive strategies for robot manipulators, the regressor-free adaptive controller design also requires applying Slotine and Li's modification to avoid the feedback of joint accelerations. In this paper, a simple method is proposed to construct a regressor-free adaptive controller for robot manipulators without Slotine and Li's modification. In the new design, the joint acceleration vector is lumped into an unknown time-varying function and the function approximation technique is utilized to cover its effect; therefore, its implementation is free from joint acceleration feedback. The closed-loop stability and boundedness of internal signals are justified by the Lyapunov-like technique. Both simulation and experimental results for a two-link robot are presented to show the effectiveness of the proposed design.