In recent years, the media industry has achieved rapid development and experienced three development stages from traditional media to new media and then to the current convergence media. Convergence media has brought about great changes in content production, communication mechanism, operation and maintenance management, but also brought about problems such as declining credibility of the industry, difficulty in confirming content rights, difficulty in protecting user privacy, etc. Research on convergence media based on blockchain can make use of the characteristics of blockchain to design or optimize the media industry. In this paper, we introduced the development of convergence media, blockchain and consensus mechanism, then we described a sustainable convergence media ecology based on blockchain. Furthermore, we designed and implemented a consensus mechanism named proof of efficiency (PoE). After analysis, PoE can provide high security and resist 51% resource attack, sybil attack, etc. The experimental results show that PoE has the characteristics of decentralization, strong consistency, low energy consumption, short average block generation time, high throughput and short block confirmation time; the consensus results of PoE can reflect the node’s ecological characteristics in convergence media which can stimulate the activity of nodes and better solve the generation of the Matthew effect.