A new adaptive control scheme for direct control of manipulator end-effector to achieve trajectory tracking in Cartesian space is developed in this paper. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory using the Lyapunov method and are not based on parameter estimation of the robot model. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload; and is computationally fast for on-line implementation