This paper illustrates the practical design procedure on a position control of an electrical fin actuator for the guided missile using Time Delay Control(TDC) and Enhanced Time Delay Observer(ETDO). Since TDC is robust to the model uncertainties such as the parameter variation and the external disturbance, it has been frequently used in nonlinear control systems. For a position control of an electrical fin actuator in the missile system, TDC requires the velocity sensor as well as the position sensor. To resolve the problems of the cost, the space and the malfunction due to the velocity sensor, ETDO is used as the velocity observer. ETDO is enhanced version of TDO that has the problems of the reconstruction errors and the restriction on selecting its gains. To maximize the control performance, the parameters of ETDO are optimized by using the genetic algorithm. The effectiveness of this approach is proved through a series of simulation studies and experiments, and the designed controller is compared with the typical TDC and TDC using the reduced oder observer.