Accurately estimating of IP Traffic matrix (TM) is still a challenging task and it has wide applications in network management, load-balancing, traffic detecting and so on. In this paper, we propose an accurate method, i.e., the Moore-Penrose inverse based neural network approach for the estimation of IP network traffic matrix with extended input and expectation maximization iteration, which is termed as MNETME for short. Firstly, MNETME adopts the extended input component, i.e., the product of routing matrix's Moore-Penrose inverse and the link load vector, as the input to the neural network....