An adaptive fuzzy controller is developed for a serial-link robot arm. The proposed rotated fuzzy basis function (RFBF) controller is a more flexible fuzzy basis function expansion to approximate unknown functions of the robot model. All parameters of RFBF network can be tuned online when the number of rules is determined. In the control design, the unmodelled dynamics are considered. Moreover, the stability analysis shows that the states and tracking errors of the robot arm are uniformly bounded. Simulations of the proposed controller on the PUMA-560 robot arm demonstrate the effectiveness.