Spatiotemporal prediction is challenging due to the complex dynamic motion and appearance changes. Existing work concentrates on embedding additional cells into the standard ConvLSTM to memorize spatial appearances during the prediction. These models always rely on the convolution layers to capture the spatial dependence, which are local and inefficient. However, long-range spatial dependencies are significant for spatial applications. To extract spatial features with both global and local dependencies, we introduce the self-attention mechanism into ConvLSTM. Specifically, a novel self-attention memory (SAM) is proposed to memorize features with long-range dependencies in terms of spatial and temporal domains. Based on the self-attention, SAM can produce features by aggregating features across all positions of both the input itself and memory features with pair-wise similarity scores. Moreover, the additional memory is updated by a gating mechanism on aggregated features and an established highway with the memory of the previous time step. Therefore, through SAM, we can extract features with long-range spatiotemporal dependencies. Furthermore, we embed the SAM into a standard ConvLSTM to construct a self-attention ConvLSTM (SA-ConvLSTM) for the spatiotemporal prediction. In experiments, we apply the SA-ConvLSTM to perform frame prediction on the MovingMNIST and KTH datasets and traffic flow prediction on the TexiBJ dataset. Our SA-ConvLSTM achieves state-of-the-art results on both datasets with fewer parameters and higher time efficiency than previous state-of-the-art method.