Shape memory alloy (SMA) actuators have attractive advantages such as high power to volume ratio. However, they also have hard nonlinearities including backlash-like hysteresis and saturation. These nonlinearities result in steady-state errors and limit cycle problems when conventional controllers are used for trajectory control. In this paper, time delay control (TDC) is applied to SMA actuators. The TDC is a well-known robust nonlinear controller and does not require a precise mathematical plant model. The dynamics of an SMA actuator was derived based on Liang's model. This dynamics does not only describe the characteristics of SMA actuators very effectively but also helps tune the TDC gains. A control strategy for the SMA actuator was established and examined from the point of view of the influence of an anti-windup scheme and high gain tuning on the control performance. We also conducted experiments on the position control of the SMA actuator and show the results of the TDC in comparison with other control schemes.