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• An edge-terminal collaborative mining task processing framework for microgrid is proposed. • A delay-and-throughput-based blockchain computing task offloading model is constructed. • Optimize the offloading decision, transmission power, as well as the generating frequency and size of blocks. In the regional distribution network, microgrid is often used to build local energy system to realize regional autonomy in the process of power generation, transmission, and consumption. Applying blockchain technology in microgrid can meet the needs of security and privacy in energy transactions, and can conduct secure point-to-point transactions between anonymous entities. However, blockchain nodes will generate numerous computing-intensive tasks in the process of mining, and cause high delay in energy transaction. Therefore, we take advantage of mobile edge computing (MEC) technology and propose an edge-terminal collaborative mining task processing framework to increase the computing ability of the blockchain system. This framework includes three working modes: local computing, user collaboration and edge node collaboration. Particularly, the trust value of collaborative user nodes is considered to avoid security threats caused by malicious nodes. Furthermore, we establish a delay-and-throughput-based blockchain computing task offloading model, and use asynchronous advantage actor-critic (A3C) algorithm to jointly optimize offloading decision, transmission power allocation, block interval and size configuration. Simulation results show that, compared with Only-MEC and Fixed-BlockSize algorithms, the proposed algorithm can reduce the average delay by 1.7% and 2.5%, and improve the average transaction throughput by 12.1% and 28.5% respectively. [ABSTRACT FROM AUTHOR]