In this paper, design of an adaptive controller, as a combination of feedback linearization technique and Lyapunov stability theory, is presented for a parallel robot. Considering a three degree-of-freedom parallel mechanism of the robot, which serves pure translational motion for its end-effector, kinematic and constraint equations are derived. Then the dynamic model of the constrained system is extracted via Lagrange’s method to be used in the robot control. Two optimized trajectories are designed for the end-effector in the presence of some obstacles using harmony search algorithm to be tracked by the robot. An objective function is defined based on achieving to the shortest path and also avoiding collisions to the obstacles keeping a marginal distance from each. The first trajectory is a 2D path with four circular obstacles and the second is a 3D path with three spherical obstacles. Performance of the designed controller is simulated and studied in conditions including external disturbances and varying system parameters. The results show that the proposed adaptive controller has a suitable performance in control of the end-effector to track the designed trajectories in spite of external disturbances and also uncertainty and variation of the model parameters.