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Accurate flood prediction is crucial for disaster prevention and mitigation. Hydrological data exhibit highly nonlinear temporal patterns and encompass complex spatial relationships between rainfall and flow. Existing flood prediction models struggle to capture these intricate temporal features and spatial dependencies. This paper presents an adaptive periodic and spatial self-attention method based on LSTM (APS-LSTM) to address these challenges. The APS-LSTM learns temporal features from a multi-periodicity perspective and captures diverse spatial dependencies from different period divisions. The APS-LSTM consists of three main stages, (i) Multi-Period Division, that utilizes Fast Fourier Transform (FFT) to divide various periodic patterns; (ii) Spatio-Temporal Information Extraction, that performs periodic and spatial self-attention focusing on intra- and inter-periodic temporal patterns and spatial dependencies; (iii) Adaptive Aggregation, that relies on amplitude strength to aggregate the computational results from each periodic division. The abundant experiments on two real-world datasets demonstrate the superiority of APS-LSTM. The code is available: https://github.com/oopcmd/APS-LSTM.