In this paper, an adaptive control system by using adaptation and robustness characteristics of Gamma neural networks for a nonlinear and unstable system will be proposed. The system which has been chosen to show the application of a Gamma neural network is an Inverted Pendulum which is a famous system for designing a controller with nonlinear and unstable properties. Step by step stages to design a neural network controller including initial stabilization of an unstable system, optimization of parameters of the network and improving robustness are investigated in detail. Results show higher applicability and adaptivity in different situations like encountering disturbance and colored noise in comparison to more common structures such as MLP and TDL networks.