Blockchain brings various advantages to online transactions. However, the total transparency of these transactions may leakage users sensitive information. Requirements on both cooperation and anonymity for companies/organizations become necessary. In this paper, we propose a Multi-center Anonymous Blockchain-based (MAB) system, with joint management for the consortium and privacy protection for the participants. To achieve that, we formalize the syntax used by the MAB system and present a general construction based on a modular design. By applying cryptographic primitives to each module, we instantiate our scheme with anonymity and decentralization. Furthermore, we carry out a comprehensive formal analysis of the proposed solution. The results demonstrate our constructed scheme is secure and efficient.