In this paper, we propose a novel adaptive control scheme for robotic systems by incorporating the parameter error into the adaptive law. By carrying out filter operations, the robotic system is linearly parameterized without using the measurements of acceleration. Then a new adaptive algorithm is introduced to guarantee that the parameter error and control error exponentially converge to zero. In particular, we provide an intuitive method to verify the standard PE condition for the parameter estimation. The robustness against disturbances is also studied and comparisons to several adaptive laws are provided. Simulations with a realistic robot arm are presented to validate the improved performance.