This paper presents NeuTM, a framework for network Traffic Matrix (TM) prediction based on Long Short-Term Memory Recurrent Neural Networks (LSTM RNNs). TM prediction is defined as the problem of estimating future network traffic matrix from the previous and achieved network traffic data. It is widely used in network planning, resource management and network security. Long Short-Term Memory (LSTM) is a specific recurrent neural network (RNN) architecture that is well-suited to learn from data and classify or predict time series with time lags of unknown size. LSTMs have been shown to model longrange dependencies more accurately than conventional RNNs. NeuTM is a LSTM RNN-based framework for predicting TM in large networks. By validating our framework on real-world data from GEANT network, we show that our model converges quickly and gives state of the art TM prediction performance.