In this paper, a linear lightweight electric cylinder constructed using shape memory alloy (SMA) is proposed. Spring SMA is used as the actuator to control the position and force of the cylinder rod. The model predictive control algorithm is investigated to compensate SMA hysteresis phenomenon and control the cylinder. In the predictive algorithm, the future output of the cylinder is computed based on the cylinder model, and the control signal is computed to minimize the error and power criterion. The cylinder model parameters are estimated by an online identification algorithm. Experimental results show that the SMA cylinder is able to precisely control position and force by using the predictive control strategy though the hysteresis effect existing in the actuator. The performance of the proposed controller is compared with that of a conventional PID controller.