Machine learning has been widely applied in structural health monitoring. While most existing methods, which are limited to forecasting structural state evolution of large infrastructures. forecast the structural state in a step-by-step manner, extracting feature of structural state trends and the negative effects of data collection under abnormal conditions are big challenges. To address these issues, a long-term structural state trend forecasting method based on long sequence time-series forecasting (LSTF) with an improved Informer model integrated with Fast Fourier transform (FFT) is proposed, named the FFT–Informer model. In this method, by using FFT, structural state trend features are represented by extracting amplitude and phase of a certain period of data sequence. Structural state trend, a long sequence, can be forecasted in a one-forward operation by the Informer model that can achieve high inference speed and accuracy of prediction based on the Transformer model. Furthermore, a Hampel filter that filters the abnormal deviation of the data sequence is integrated into the Multi-head ProbSparse self-attention in the Informer model to improve forecasting accuracy by reducing the effect of abnormal data points. Experimental results on two classical data sets show that the FFT–Informer model achieves high and stable accuracy and outperforms the comparative models in forecasting accuracy. It indicates that this model can effectively forecast the long-term state trend change of a structure and is proposed to be applied to structural state trend forecasting and early damage warning.