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The existing federated learning framework is based on the centralized model coordinator, which still faces serious security challenges such as device differentiated computing power, single point of failure, poor privacy, and lack of Byzantine fault tolerance. In this paper, we propose an asynchronous federated learning system based on permissioned blockchains, using permissioned blockchains as the federated learning server, which is composed of a main-blockchain and multiple sub-blockchains, with each sub-blockchain responsible for partial model parameter updates and the main-blockchain responsible for global model parameter updates. Based on this architecture, a federated learning asynchronous aggregation protocol based on permissioned blockchain is proposed that can effectively alleviate the synchronous federated learning algorithm by integrating the learned model into the blockchain and performing two-order aggregation calculations. Therefore, the overhead of synchronization problems and the reliability of shared data is also guaranteed. We conducted some simulation experiments and the experimental results showed that the proposed architecture could maintain good training performances when dealing with a small number of malicious nodes and differentiated data quality, which has good fault tolerance, and can be applied to edge computing scenarios. [ABSTRACT FROM AUTHOR]