Blockchain, as a distributed database, has been wildly used in real-world applications. Different systems based on blockchain form data silos. Therefore, cross-chain data transmission is required to realize value transfer in different systems. In the process of cross-chain data transmission, authentication is important for data security. In this work, we design an auditable anonymous authentication scheme for cross-chain data transmission. In our scheme, the sender can generate anonymous authentication message on the data. Then the receiver of the target blockchain knows the data is sent by a legal user of the original blockchain, but cannot know the real identity of the sender. By using Trusted Execution Environment (TEE) and pseudo identity methods, our scheme is more efficient than the similar anonymous authentication schemes in blockchain.