Precipitation nowcasting is an important task, which can serve numerous applications such as urban alert and transportation. Previous studies leverage convolutional recurrent neural networks (RNNs) to address the problem. However, they all suffer from two inherent drawbacks of the convolutional RNN, namely, the lack of a memory cell to preserve the fine-grained spatial appearances and the position misalignment issue when combining current observations with previous hidden states. In this article, we aim to overcome the defects. Specifically, we propose a novel pseudo flow spatiotemporal LSTM unit (PFST-LSTM), where a spatial memory cell and a position alignment module are developed and embedded in the structure of LSTM. Upon the PFST-LSTM units, we develop a new sequence-to-sequence architecture for precipitation nowcasting, which can effectively combine the spatial appearances and motion information. Extensive empirical evaluations are conducted on synthetic MovingMNIST++ and CIKM AnalytiCup 2017 datasets. Our experimental results demonstrate the superiority of the proposed PFST-LSTM over the state-of-the-art competitors. To reproduce the results, we release the source code at: https://github.com/luochuyao/PFST-LSTM.