Generalized few-shot node classification (GFS-NC) is a very important challenge for graph-based algorithms, as it requires to identify novel classes and base classes simultaneously. Although there are several methods that try to combine metalearning or metric learning with graph neural networks to solve few-shot problem, most of them assume that test samples only come from the novel classes, which is impractical in reality. Besides, they overlook the relationship among classes, which can provide additional information for the novel classes classification. In this article, we propose a graph-based knowledge distillation network (GraphKD) to extract the class relationship and learn better nodes representations for nodes from novel classes in GFS-NC task. GraphKD consists of two modules: balanced pretraining module and class-relation transferring module. Balanced pretraining can optimize network parameters to a suitable manifold for subsequent initialization. The class-relation transferring module leverages a knowledge distillation model, where a teacher model generates soft labels containing interclass relationships and then transfer them to the student model. The student model is optimized to fit both the soft labels and hard labels concurrently. This relationship information can help the student model better understand the similarities and differences between classes, thereby improving its classification performance. In addition, we employee information entropy to distinguish the samples locate at the boundary of a base class and novel class and then assign them larger weights in the student model to enhance its expressive capacity for novel nodes. Our experiments show that the proposed method outperforms state-of-the-art baselines on various few-shot node classification datasets.