Cross-chain communication is the cryptographic technology that sends and receives tokens or data among multiple blockchains. A parent-child blockchain system is one of the methods of cross-chain communication. Existing studies apply Byzantine fault-tolerant (BFT) mechanisms to achieve consensus among multiple N blockchains. However, cross-chain communication based on PBFT requires \(\mathcal {O}(N^2)\) communication complexity to achieve consensus mechanisms among multiple N blockchains (no scalability). In addition, existing cross-chain communication do not propose a scheme to prevent a malicious act by users who mediate tokens (no security). Furthermore, there is no existing scheme that simultaneously satisfies unforgeability, which prevents the sender of a token from forging the sent token, and unlinkability, which protects the privacy of the sender and receiver (no unlinkability and no unforgeability). In this paper, we propose a Privacy-Preserving Scalable Cross-Chain Communication (PPSCCC) among multiple blockchains that solve the above problems. In PPSCCC, by applying the commitment scheme to the token mediators, the communication complexity among blockchains for consensus mechanism can be achieved with \(\mathcal {O}(N)\) . We also prove unlinkability and unforgeability by using the hiding and binding properties of the commitment scheme. In addition, by introducing Proof of Commitment Reputation ( \(\textsf{PoCR}\) ), we achieve a scheme to prevent malicious behavior of users who mediate tokens. We then implement our proposed scheme. Finally, we compare our scheme with existing schemes to highlight the strengths of our scheme and show that our scheme is more practical.