In this paper, we propose a novel variant of the algorithm to improve the generalization performance for Elman neural networks (ENN). Here, the weight decay term, also called L2 regularization, which can effectively control the value of weights excessive growth, also over-fitting phenomenon can be effectively prevented. The main contribution of this work lies in that we have conducted a rigorous theoretical analysis of the proposed approach, i.e. the weak and strong convergence results are obtained. The comparison experiments to the problems of function approximation and classification on the real-world data have been performed to verify the theoretical results.