The issue of privacy leakage in distributed consensus has garnered significant attention over the years, but existing studies often overlook the challenges posed by limited communication in algorithm design. This paper addresses the issue of privacy preservation in distributed weighted average consensus under limited communication scenarios. Specifically targeting directed and unbalanced topologies, we propose a privacy-preserving implementation protocol that incorporates the Paillier homomorphic encryption scheme. The protocol encrypts only the 1-bit quantized messages exchanged between agents, thus ensuring both the correctness of the consensus result and the confidentiality of each agent’s initial state. To demonstrate the practicality of the proposed method, we carry out numerical simulations that illustrate its ability to reach consensus effectively while ensuring the protection of private information.