Effective feature extraction is a key issue in hyperspectral image (HSI) classification task. Recent works have studied hyperspectral classification models based on various deep architectures. However, the specific architecture cannot fully exploit the complementary diversity of global and local features in HSIs, resulting in suboptimal results. To address these issues, we fully utilize the advantages of GNN and CNN in global and local feature extraction and design a new end-to-end global–local feature fusion enhancement network (GLFFEN). Specifically, we first construct a GNN with dynamically weighted neighbor contributions using superpixel-segmented patches as nodes, named the Graph Attention (GA) branch. Additionally, we design a spatial–spectral feature attention module (SSFAM) to enhance the ability of the CNN to extract spatial and spectral features in local neighborhoods, termed the spatial–spectral feature attention (SSFA) branch. Moreover, a multi-feature adaptive fusion (MAF) module is proposed to solve the problem of weight distribution during global–local feature fusion. Experiments on three well-known HSI datasets have shown that our GLFFEN surpasses state-of-the-art (SOTA) methods on three widely used metrics.