Over the past few years, deep learning has been introduced to tackle hyperspectral image (HSI) classification and demonstrated good performance. In particular, the convolutional neural network (CNN) based methods have progressed. However, due to the high dimensionality of HSI and equal treatment of all bands, the performances of CNN based methods are hampered. The labels of land-covers often differ between edge and the center pixels in pixel-centered spatial information. These edge pixels may weaken the discrimination of spatial features and reduce classification accuracy. Motivated by the attention mechanism of the human visual system, the spatial proximity feature selection with residual spatial-spectral attention network is proposed in this article. It contains a residual spatial attention module, a residual spectral attention module, and a spatial proximity feature selection module. The residual spatial attention module aims to select the crucial spatial information, which assigns weights to different features by measuring the similarity between the surrounding elements and their central ones. The residual spectral attention module is designed for spectral bands which are selected from raw input data by emphasizing the valuable bands and suppressing the valueless. According to the spatial distribution of features, the spatial proximity feature selection module is used to filter features effectively. Experiments on three public data sets demonstrate that the proposed network outperforms the state-of-the-art methods in comparison.