Data-driven saliency detection has attracted strong interest as a result of applying convolutional neural networks to the detection of eye fixations. Although a number of image-based salient object and fixation detection models have been proposed, video fixation detection still requires more exploration. Different from image analysis, motion and temporal information is a crucial factor affecting human attention when viewing video sequences. Although existing models based on local contrast and low-level features have been extensively researched, they failed to simultaneously consider interframe motion and temporal information across neighboring video frames, leading to unsatisfactory performance when handling complex scenes. To this end, we propose a novel and efficient video eye fixation detection model to improve the saliency detection performance. By simulating the memory mechanism and visual attention mechanism of human beings when watching a video, we propose a step-gained fully convolutional network by combining the memory information on the time axis with the motion information on the space axis while storing the saliency information of the current frame. The model is obtained through hierarchical training, which ensures the accuracy of the detection. Extensive experiments in comparison with 11 state-of-the-art methods are carried out, and the results show that our proposed model outperforms all 11 methods across a number of publicly available datasets.