The development of a position control system for a shape memory alloy (SMA) wire actuator using an electrical resistance feedback is presented in this paper. A novel control scheme is implemented to eliminate the need for a position sensor to achieve stable and accurate positioning by utilizing the actuator's electrical resistance feedback. Experiments are conducted to investigate the relationship between electrical resistance and displacement using an SMA wire test setup. Due to the highly nonlinear behavior of the SMA actuator, a neural network is employed to model the relationship and to predict the position of the actuator using only the electrical resistance. Feedback control of the SMA is achieved by using a proportional-derivative (PD) controller. Experimental results demonstrate that the proposed position control system achieves good control performance without using a position sensor.