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A well-informed recommendation framework could not only help users identify their interested items, but also benefit the revenue of various online platforms (e.g., e-commerce, social media). Traditional recommendation models usually assume that only a single type of interaction exists between user and item, and fail to model the multiplex user-item relationships from multi-typed user behavior data, such as page view, add-to-favourite and purchase. While some recent studies propose to capture the dependencies across different types of behaviors, two important challenges have been less explored: i) Dealing with the sparse supervision signal under target behaviors (e.g., purchase). ii) Capturing the personalized multi-behavior patterns with customized dependency modeling. To tackle the above challenges, we devise a new model CML, Contrastive Meta Learning (CML), to maintain dedicated cross-type behavior dependency for different users. In particular, we propose a multi-behavior contrastive learning framework to distill transferable knowledge across different types of behaviors via the constructed contrastive loss. In addition, to capture the diverse multi-behavior patterns, we design a contrastive meta network to encode the customized behavior heterogeneity for different users. Extensive experiments on three real-world datasets indicate that our method consistently outperforms various state-of-the-art recommendation methods. Our empirical studies further suggest that the contrastive meta learning paradigm offers great potential for capturing the behavior multiplicity in recommendation. We release our model implementation at: https://github.com/weiwei1206/CML.git.