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In this paper, a novel neural network named CRSum for the video summarization task is proposed. The proposed network integrates feature extraction, temporal modeling, and summary generation into an end-to-end architecture. Compared with previous work on this task, the proposed method owns three distinctive characteristics: 1) it for the first time leverages convolutional recurrent neural network for simultaneously modeling spatial and temporal structure of video for summarization; 2) thorough and delicate features of video are obtained in the proposed architecture by trainable three-dimension convolutional neural networks and feature fusion; and 3) a new loss function named Sobolev loss is defined, aiming to constrain the derivative of sequential data and exploit potential temporal structure of video. A series of experiments are conducted to prove the effectiveness of the proposed method. We further analyze our method from different aspects by well-designed experiments.