In recent years, supervised video summarization has achieved promising progress with various recurrent neural networks (RNNs) based methods, which treats video summarization as a sequence-to-sequence learning problem to exploit temporal dependency among video frames across variable ranges. However, RNN has limitations in modelling the long-term temporal dependency for summarizing videos with thousands of frames due to the restricted memory storage unit. Therefore, in this paper we propose a stacked memory network called SMN to explicitly model the long dependency among video frames so that redundancy could be minimized in the video summaries produced. Our proposed SMN consists of two key components: Long Short-Term Memory (LSTM) layer and memory layer, where each LSTM layer is augmented with an external memory layer. In particular, we stack multiple LSTM layers and memory layers hierarchically to integrate the learned representation from prior layers. By combining the hidden states of the LSTM layers and the read representations of the memory layers, our SMN is able to derive more accurate video summaries for individual video frames. Compared with the existing RNN based methods, our SMN is particularly good at capturing long temporal dependency among frames with few additional training parameters. Experimental results on two widely used public benchmark datasets: SumMe and TVsum, demonstrate that our proposed model is able to clearly outperform a number of state-of-the-art ones under various settings.