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This paper introduces a novel and efficient graph convolutional network (GCN) and Spatial Supporting Modification (SSM) based method for hyperspectral images (HSI) classification, which is named as Spatial First (SPA-F) and it can fully utilize the spatial information based on the assumption that neighboring pixels are more likely to be the same category. The proposed method uses the spatial information from two levels, and consists of the following steps: Firstly, constructing all non-background pixels as a graph. Secondly, training and testing a Graph Convolution Network (GCN) to perform node classification task based on the constructed graph. Thirdly, locating the spatial supporting pixels for all nonbackground pixels according to the spatial position in the HSI. Finally, the proposed SSM strategy is used to fine tune the initial classification results obtained in the second step. The superiorities of the proposed method are verified on Indian Pines and SalinasA scene datasets even when the number of training samples is small. INDEX TERMS Spatial first, spatial supporting, hyperspectral images (HSI), graph convolution network (GCN).