Deep learning has achieved enormous success in various computer tasks. The excellent performance depends heavily on adequate training datasets, however, it is difficult to obtain abundant samples in practical applications. Few-shot learning is proposed to address the data limitation problem in the training process, which can perform rapid learning with few samples by utilizing prior knowledge. In this paper, we focus on few-shot classification to conduct a survey about the recent methods. First, we elaborate on the definition of the few-shot classification problem. Then we propose a newly organized taxonomy, discuss the application scenarios in which each method is effective, and compare the pros and cons of different methods. We classify few-shot image classification methods from four perspectives: (i) Data augmentation, which contains sample-level and task-level data augmentation. (ii) Metric-based method, which analyzes both feature embedding and metric function. (iii) Optimization method, which is compared from the aspects of self-learning and mutual learning. (iv) Model-based method, which is discussed from the perspectives of memory-based, rapid adaptation and multi-task learning. Finally, we conduct the conclusion and prospect of this paper.