Input time delay systems have many applications in the industry. The delay in input may be caused by communication signals, command signals or an intrinsic characteristic of a system. So it is important to offer some methods for the control of input delay systems. The main problem in the stability of input delay systems is the existence of time lag in system input. This prevents using input in real time. Therefore it is necessary to solve this problem to have a reliable controller. There are many suggestions for solving this problem. One suggestion is to derive a prediction model which forecasts the system states. This model should compensate for the input time lag. One such model is known as Artstien model which is used by many designers. Artstien model, however, has no feedback from the system and is based on its time domain solution. There are some examples that show the stability of the closed-loop system can not be achieved by this method. In this thesis, a new prediction model is presented for input time delay systems. This model is based on observer structure introduced in modern control. It is proved that the prediction error converges to zero asymptotically. The existance of feedback in the proposed model is one of its advantages. This model is derived for different linear input delay systems. A controller is also designed based on this model and the closed-loop system stability is proved for each case.