In recent years, graph convolutional networks (GCNs) have attracted increasing attention in hyperspectral image (HSI) classification owing to their exceptional representation capabilities. However, the high computational requirements of GCNs have led most existing GCN-based HSI classification methods to utilize superpixels as graph nodes, thereby limiting the spatial topology scale and neglecting pixel-level spectral–spatial features. To address these limitations, we propose a novel HSI classification network based on graph convolution called the spatial-pooling-based graph attention U-net (SPGAU). Specifically, unlike existing GCN models that rely on fixed graphs, our model involves a spatial pooling method that emulates the region-growing process of superpixels and constructs multi-level graphs by progressively merging adjacent graph nodes. Inspired by the CNN classification framework U-net, SPGAU’s model has a U-shaped structure, realizing multi-scale feature extraction from coarse to fine and gradually fusing features from different graph levels. Additionally, the proposed graph attention convolution method adaptively aggregates adjacency information, thereby further enhancing feature extraction efficiency. Moreover, a 1D-CNN is established to extract pixel-level features, striking an optimal balance between enhancing the feature quality and reducing the computational burden. Experimental results on three representative benchmark datasets demonstrate that the proposed SPGAU outperforms other mainstream models both qualitatively and quantitatively.