Few-shot learning (FSL) aims to recognize a novel class with very few instances, which is a challenging task since it suffers from a data scarcity issue. One way to effectively alleviate this issue is introducing explicit knowledge summarized from human past experiences to achieve knowledge transfer for FSL. Based on this idea, in this paper, we introduce the explicit knowledge of class hierarchy (i.e., the hierarchy relations between classes) as FSL priors and propose a novel hyperbolic knowledge transfer framework for FSL, namely, HyperKT. Our insight is, in the hyperbolic space, the hierarchy relation between classes can be well preserved by resorting to the exponential growth characters of hyperbolic volume, so that better knowledge transfer can be achieved for FSL. Specifically, we first regard the class hierarchy as a tree-like structure. Then, 1) a hyperbolic representation learning module and a hyperbolic prototype inference module are employed to encode/infer each image and class prototype to the hyperbolic space, respectively; and 2) a novel hierarchical classification and relation reconstruction loss are carefully designed to learn the class hierarchy. Finally, the novel class prediction is performed in a nearest-prototype manner. Extensive experiments on three datasets show our method achieves superior performance over state-of-the-art methods, especially on 1-shot tasks.