Few-shot learning aims to recognize new concepts from very few examples. However, most of the existing few-shot learning methods mainly concentrate on the first-order statistic of concept representation or a fixed metric on the relation between a sample and a concept. In this work, we propose a novel end-to-end deep architecture, named Covariance Metric Networks (CovaMNet). The CovaMNet is designed to exploit both the covariance representation and covariance metric based on the distribution consistency for the few-shot classification tasks. Specifically, we construct an embedded local covariance representation to extract the second-order statistic information of each concept and describe the underlying distribution of this concept. Upon the covariance representation, we further define a new deep covariance metric to measure the consistency of distributions between query samples and new concepts. Furthermore, we employ the episodic training mechanism to train the entire network in an end-to-end manner from scratch. Extensive experiments in two tasks, generic few-shot image classification and fine-grained fewshot image classification, demonstrate the superiority of the proposed CovaMNet. The source code can be available from https://github.com/WenbinLee/CovaMNet.git.