This paper addresses the problem of supervised video summarization by formulating it as a sequence-to-sequence learning problem, where the input is a sequence of original video frames, and the output is a keyshot sequence. Our key idea is to learn a deep summarization network with attention mechanism to mimic the way of selecting the keyshots of human. To this end, we propose a novel video summarization framework named attentive encoder-decoder networks for video summarization (AVS), in which the encoder uses a bidirectional long short-term memory (BiLSTM) to encode the contextual information among the input video frames. As for the decoder, two attention-based LSTM networks are explored by using additive and multiplicative objective functions, respectively. Extensive experiments are conducted on two video summarization benchmark datasets, i.e., SumMe and TVSum. The results demonstrate the superiority of the proposed AVS-based approaches against the state-of-the-art approaches, with remarkable improvements on both datasets.