The dynamic nature of social networks has a huge impact on temporal link prediction problem, in which we are given snapshots of a network at different timestamps and need to predict the possible link between a node pair in the future or whether there are some missing links. The core issue is how to effectively use topology and timing information to improve performance. This paper proposes a model called NeLSTM combining network embedding with Long Short-Term Memory(LSTM) network to predict temporal network topology structure, which is represented by node vectors. First, to measure the impact of a past link on the future network, we add a time attenuation coefficient to the weight of a node pair. Then, network embedding is able to preserve the network topology information and based on its output, LSTM can characterize the continuous network evolution. Finally, NeLSTM obtains the similarity of a node pair via calculating the inner product, which exactly represents the possibility that a link occurs. Experimental results show that NeLSTM performs well in real world networks.