Few-shot learning aims at simulating the ability of human beings to quickly learn new things with only few samples, which is of great significance for deep learning tasks when samples are limited. However, in many practical tasks with limited computing resources, the model scale may still limit a wider application of few-shot learning. This study presents a realistic requirement for lightweight tasks for few-shot learning. As a widely used auxiliary strategy in deep learning, knowledge distillation transfers knowledge between models by using additional supervised information, which has practical application in both improving model accuracy and reducing model scale. This study first verifies the effectiveness of the knowledge distillation strategy in model lightweight for few-shot learning. Then according to the characteristics of few-shot learning, two new distillation methods for few-shot learning are designed: (1) distillation based on image local features; (2) distillation based on auxiliary classifiers. Experiments on miniImageNet and TieredImageNet datasets demonstrate that the new distillation methods are significantly superior to traditional knowledge distillation in few-shot learning tasks. The source code is available from https://github.com/cjy97/FSLKD.