Abstract: An algorithm for computing Lyapunov exponents of a dynamical system based on radial basis function(RBF) neural networks is proposed. An RBF network structure is designed. The formula of the Lyapunov exponents based on an RBF network is derived. Simulations show that compared with the other existing algorithms, the proposed algorithm has higher accuracy and convergence speed, and it needs much less observed samples. It is demonstrated that the proposed algorithm can compute the Lyapunov exponents of a dynamical system more accurately and rapidly.