Traffic prediction plays an important role in evaluating the performance of telecommunication networks and attracts intense research interests. A significant number of algorithms and models have been put forward to analyse traffic data and make prediction. In the recent big data era, deep learning has been exploited to mine the profound information hidden in the data. In particular, Long Short-Term Memory (LSTM), one kind of Recurrent Neural Network (RNN) schemes, has attracted a lot of attentions due to its capability of processing the long-range dependency embedded in the sequential traffic data. However, LSTM has considerable computational cost, which can not be tolerated in tasks with stringent latency requirement. In this paper, we propose a deep learning model based on LSTM, called Random Connectivity LSTM (RCLSTM). Compared to the conventional LSTM, RCLSTM makes a notable breakthrough in the formation of neural network, which is that the neurons are connected in a stochastic manner rather than full connected. So, the RCLSTM, with certain intrinsic sparsity, have many neural connections absent (distinguished from the full connectivity) and which leads to the reduction of the parameters to be trained and the computational cost. We apply the RCLSTM to predict traffic and validate that the RCLSTM with even 35% neural connectivity still shows a satisfactory performance. When we gradually add training samples, the performance of RCLSTM becomes increasingly closer to the baseline LSTM. Moreover, for the input traffic sequences of enough length, the RCLSTM exhibits even superior prediction accuracy than the baseline LSTM.