In this paper, dynamic modeling and control of a three-degrees-of-freedom parallel robot with pure translational motion is performed. Constraint equations are derived based on the kinematic model of the robot and Lagrange method is applied to derive the dynamic equations. In order to control the robot position on planned reference trajectories, in presence of uncertainties of the dynamic model, a sliding mode controller is designed which is robust against the uncertainties and induced noises. Performance of the designed controller is simulated and evaluated in different conditions including the presence of noise and parameters variation. In this regard, a comparison has been made between the response of the proposed sliding mode controller and response of a feedback linearization controller, indicating their capabilities in noise rejection and compensation of parameters variation. Also, the effect of defining different sliding surfaces on the performance of the sliding mode controller, and using the integral of error instead of the error itself, have been studied and examined. Results show that the proposed sliding mode controller has a desirable performance in tracking the reference trajectories in presence of the model uncertainties and noise for this kind of parallel mechanism.