The core idea of metric-based few-shot image classification is to directly measure the relations between query images and support classes to learn transferable feature embeddings. Previous work mainly focuses on image-level feature representations, which actually cannot effectively estimate a classs distribution due to the scarcity of samples. Some recent work shows that local descriptor based representations can achieve richer representations than image-level based representations. However, such works are still based on a less effective instance-level metric, especially a symmetric metric, to measure the relations between query images and support classes. Given the natural asymmetric relation between a query image and a support class, we argue that an asymmetric measure is more suitable for metric-based few-shot learning. To that end, we propose a novel Asymmetric Distribution Measure (ADM) network for few-shot learning by calculating a joint local and global asymmetric measure between two multivariate local distributions of queries and classes. Moreover, a task-aware Contrastive Measure Strategy (CMS) is proposed to further enhance the measure function. On popular miniImageNet and tieredImageNet, we achieve $3.02%$ and $1.56%$ gains over the state-of-the-art method on the $5$-way $1$-shot task, respectively, validating our innovative design of asymmetric distribution measures for few-shot learning.