This paper presents a new computational algorithm of the model-based adaptive manipulator control, adopting the basic method proposed by Slotine and Li (1987). The manipulator regressor that is represented by an actual velocity vector and a reference velocity vector is computed explicitly by a recursive algorithm based on the Newton-Euler formulation. The proposed algorithm is more efficient than other methods for a manipulator with six or fewer joints. An experimental result is also presented to show the possibility of an adaptive controller having a single DSP for a robot manipulator with six degrees of freedom.