Hyperspectral image (HSI) classification has attracted much attention in the field of remote sensing. However, the lack of sufficient labeled training samples is a huge challenge for HSI classification. To face this challenge, we propose a semisupervised HSI classification method based on graph convolutional broad network (GCBN). First, to avoid the underfitting problem caused by the insufficient linear sparse feature representation ability of broad learning system (BLS), graph convolution operation is applied to extract nonlinear and discriminative spectral-spatial features from the original HSI to replace the linear mapping features in the traditional BLS. Second, to solve the problem of insufficient model classification ability caused by limited labeled samples, the combinatorial average method (CAM) is proposed to use valuable paired samples to generate sample expansion set for GCBN model training. Third, BLS is used to perform broad expansion on spectral-spatial features extracted by GCN and extended by CAM, which further enhances the feature representation ability. Finally, the output weights can be easily calculated by the ridge regression theory. Experimental results on three real HSI datasets demonstrate the effectiveness of our proposed GCBN.