Collaborative perception enables the multi-agent systems to break through the limited local perception, achieving robust and comprehensive understanding in complicated scenes. However, collaborative perception renders high communication overhead and is constrained in the real-world applications, especially those with limited bandwidth, such as subterranean exploration and marine survey. This paper proposes a communication-efficient multi-agent collaborative perception method, supported by vector quantization and entropy coding and offering significantly reduced bandwidth requirement. The proposed method employs well designed vector quantization, which achieves semantic compression with stable training process. Moreover, we incorporate entropy coding to multi-agent collaboration for the first time, which dramatically reduces the statistical redundancy. Experiments show that our method achieves superior efficiency in utilizing the bandwidth, compared with the existing methods, which achieves a more than 55% reduction in BD-rate.