Stationarity is fundamental for time-series modeling and prediction. In this article, we focus on the radial basis function network-based autoregressive (RBF-AR) models which have been widely used in practical applications. Compared to previous work, we give a less-restrictive sufficient condition for the asymptotic stationarity of the RBF-AR model. The parameter estimation of the RBF-AR model is converted to the optimization of a variable projection functional with constraints of stationarity to always derive a stationary model. The constrained evolutionary algorithm is used to solve the optimization problem. Numerical results demonstrate the effectiveness of the proposed method.