The deep learning model has been used to predict the variation rule of the target series of multivariate time series data. Based on the attention mechanism, the influence information of multiple non-predictive time series on target series in different time stages is processed as the same weight in the previous studies. However, on real-world datasets, multiple non-predictive time series has different influence (such as different mutation information) on target series in different time stages. Therefore, a new multistage attention network is designed to capture the different influence. The model is mainly composed of the influential attention mechanism and temporal attention mechanism. In the influential attention mechanism, the same and different time stage attention mechanisms are used to capture the influence information of different non-predictive time series on the target series over time. In the temporal attention mechanism, the variation law of data can be captured over time. Besides, the prediction performance of proposed model on two different real-world multivariate time series datasets is comprehensively evaluated. The results show that, the prediction performance of the proposed model beat all baseline models and SOTA models. In a word, the multistage attention network model can effectively learn the information of the influence of different non-predictive time series on the target series in different time stages in the historical data.