The long short-term memory network (LSTM) is widely used in time series data processing as a temporal recursive network. The resting-state functional magnetic resonance data shows that not only are there temporal variations in the resting state, but there are also interactions between brain regions. To integrate the temporal and spatial characteristics of brain regions, this paper proposes a model called feature weighted-LSTM (FW-LSTM). The feature weight is defined by spatial characteristics calculating the frequency of connectivity of each brain region and further integrated into the LSTM. Thus, it can comprehensively model both temporal and spatial changes in rs-fMRI brain regions. The FW-LSTM model on the Alzheimer’s disease neuroimaging initiative (ADNI) dataset is used to extract the time-varying characteristics of 90 brain regions for Alzheimer’s disease (AD) classification. The model performances are 77.80%, 76.41%, and 78.81% in accuracy, sensitivity, and specificity. It outperformed the one-dimensional convolutional neural networks (1D-CNN) model and LSTM model, which only used temporal features of brain regions.