In this paper, a finite time continuous terminal sliding mode controller with perturbation estimation for a Stewart platform is developed. Based on the robot's dynamic model, which was formulated in the active joint space, a continuous sliding mode type control law was designed to specify a finite time reaching law and a finite time sliding surface. In addition, it incorporates an estimated uncertainty term that compensates for the un-modeled dynamics, and time-varying external disturbances, therefore improving the controller's robustness. The stability analysis is performed using the Lyapunov theory. The effectiveness of the controller is verified through simulation in comparison with a computed-torque controller, in case there are model parameter variations and time-varying uncertainties. The simulation results show that the proposed controller has a superior performance of small tracking errors (nearly 10 times smaller) to that a computed torque method, and it is free chattering and robust to model parameter variations (up to 30%) and time-varying uncertainties.