A novel learning algorithm is proposed for nonlinear modelling and identification using radial basis function neural networks. The proposed method simplifies neural network training through the use of an adaptive computation algorithm (ACA). In addition, the convergence of the ACA is analyzed by the Lyapunov criterion. The proposed algorithm offers two important advantages. First, the model performance can be significantly improved through ACA, and the modelling error is uniformly ultimately bounded. Secondly, the proposed ACA can reduce computational cost and accelerate the training speed. The proposed method is then employed to model classical nonlinear system with limit cycle and to identify nonlinear dynamic system, exhibiting the effectiveness of the proposed algorithm. Computational complexity analysis and simulation results demonstrate its effectiveness.