Abstarct: This thesis, considers a single-shaft gas turbine and propose an observer-baxsed and adaptive neural network controller. This controls the rotational speed of considered gas turbine. The structure of this controller is fully explained and the control goal is the design of a system so that a gas turbine speed can detect desired input.Since ,all of the state variables are not available, the system state vector is estimated by the observer and is used to set the controller parameters and estimate the nonlinear dynamics of gas turbine with two RBF neural networks. Every gas turbine parameters including: inlet and outlet temperature, outlet pressure, inlet pressure, combustion conditions, and etc must be placed within their permitted limits, so the controller is set in accordance with the requirements of the gas turbine and its constraints and certain control goals. Finally, the controller performance was investigated to control the rotational speed of the gas turbine and the results showed that this controller could track changes in the input with a very good accuracy and speed.