Few-shot learning (FSL) aims to learn a model that can identify unseen classes using only a few training samples from each class. Most of the existing FSL methods adopt a manually predefined metric function to measure the relationship between a sample and a class, which usually require tremendous efforts and domain knowledge. In contrast, we propose a novel model called automatic metric search (Auto-MS), in which an Auto-MS space is designed for automatically searching task-specific metric functions. This allows us to further develop a new searching strategy to facilitate automated FSL. More specifically, by incorporating the episode-training mechanism into the bilevel search strategy, the proposed search strategy can effectively optimize the network weights and structural parameters of the few-shot model. Extensive experiments on the miniImageNet and tieredImageNet datasets demonstrate that the proposed Auto-MS achieves superior performance in FSL problems.