In this paper, an Evolving Neural Network Controller(ENNC) which its structure and its connection weights are optimized simultaneously by Real Variable Elitist Genetic Algoithm(RVEGA) was presented for stabilization of an Inverter Pendulum(IP) system with nonlinearity. This proposed ENNC was described by a simple genetic chromosome. And the deletion of neuron, the determinations of input or output neuron, the deleted neuron and the activation functions types are given according to the various flag types. Therefore, the connection weights, its structure and the neuron types in the given ENNC can be optimized by the proposed evolution strategy. Through the simulations, we showed that the finally acquired optimal ENNC was successfully applied to the stabilization control of an IP system.