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Cross-chain technology facilitates the interoperability among isolated blockchains on which users can freely communicate and transfer values. Existing cross-chain protocols suffer from the scalability problem when processing on-chain transactions. Off-chain channels, as a promising blockchain scaling technique, can enable micro-payment transactions without involving on-chain transaction settlement. However, existing channel schemes can only be applied to operations within a single blockchain, failing to support cross-chain services. Therefore in this paper, we propose Cross-Channel, the first off-chain channel to support cross-chain services. We introduce a novel hierarchical channel structure, a new hierarchical settlement protocol, and a smart general fair exchange protocol, to ensure scalability, fairness, and atomicity of cross-chain interactions. Besides, Cross-Channel provides strong security and practicality by avoiding high latency in asynchronous networks. Through a 50-instance deployment of Cross-Channel on AliCloud, we demonstrate that Cross-Channel is well-suited for processing cross-chain transactions in high-frequency and large-scale, and brings a significantly enhanced throughput with a small amount of gas and delay overhead.