With the growing demand for cross-platform collaboration in blockchain systems, cross-chain interoperability mechanisms have attracted widespread attention. However, the lack of trust among cross-chain entities poses serious challenges to the privacy protection of inter-chain data. Attribute-based access control (ABAC) enables fine-grained and flexible permission management, but existing schemes often disclose policies and attributes in plaintext, making it easier for attackers to exploit public on-chain information to launch attacks. To address this issue, this paper proposes a cross-chain access control scheme that combines ABAC with threshold fully homomorphic encryption (ThFHE). The scheme utilizes Cheon–Kim–Kim–Song (CKKS), a widely-used fully homomorphic encryption (FHE) scheme, to encrypt access policies and user attributes. Benefiting from the properties of FHE, smart contracts can perform permission verification directly in the ciphertext domain without exposing any sensitive information. Furthermore, the scheme achieves decentralized collaborative decryption by aggregating the partial decryption results from multiple relay nodes. Experimental results demonstrate that the scheme achieves secure and efficient cross-chain data access control with reasonable computational overhead.