The aim of this study is to present a stability in a two-dimensional dynamical system of endogenous growth with public capital. We assume the simple model of the economic growth, in which both private and public capital can influence on the rate of growth of knowledge. The public capital is rival but non excludable goods, i.e. there is a congestion in use of public capital. The model of growth is formulated as a two-dimensional dynamical system. Using mathematical methods of dynamical systems, we analyze growth paths as well as the stationary states of the system and their stability.