Effective traffic matrix estimation is the basis of efficient traffic engineering, and therefore, quality of service provision support in IP networks. In this study, trafficmatrix estimation is investigated in IP networks and an Elman neural network-based traffic matrix inference (ENNTMI) method is proposed. In ENNTMI,the conventional Elman neural network is modified to capture the spatio-temporal correlations and the time-varying property, and certain side information is introduced to help estimate traffic matrix in a network accurately. The regular parameter is further introduced into the optimal equation. Thus, the highly ill-posed nature of traffic matrix estimation is overcome effectively and efficiently.