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Deep Convolutional Neural Networks (CNNs) are powerful models that have achieved excellent performance on difficult computer vision tasks. Although CNNs perform well whenever large labeled training samples are available, they work badly on video frame synthesis due to objects deforming and moving, scene lighting changes, and cameras moving in video sequence. In this paper, we present a novel and general end-to-end architecture, called convolutional Transformer or ConvTransformer, for video frame sequence learning and video frame synthesis. The core ingredient of ConvTransformer is the proposed attention layer, i.e., multi-head convolutional self-attention layer, that learns the sequential dependence of video sequence. ConvTransformer uses an encoder, built upon multi-head convolutional self-attention layer, to encode the sequential dependence between the input frames, and then a decoder decodes the long-term dependence between the target synthesized frames and the input frames. Experiments on video future frame extrapolation task show ConvTransformer to be superior in quality while being more parallelizable to recent approaches built upon convolutional LSTM (ConvLSTM). To the best of our knowledge, this is the first time that ConvTransformer architecture is proposed and applied to video frame synthesis.