In the dense data communication environment of 5G wireless networks, with the dramatic increase in the amount of request computation tasks generated by intelligent wireless mobile nodes, its computation ability cannot meet the requirements of low latency and high reliability. Mobile edge computing (MEC) can utilize its servers with mighty computation power and closer to tackle the computation tasks offloaded by the wireless node (WN). The physical location of the MEC server is closer to WN, thereby meeting the requirements of low latency and high reliability. In this paper, we implement an MEC framework with multiple WNs and multiple MEC servers, which consider the randomness and divisibility of arrival request tasks from WN, the time-varying channel state between WN and MEC server, and different priorities of tasks. In the proposed MEC system, we present a decentralized multi-agent deep reinforcement learning-based partial task offloading and resource allocation algorithm (DeMADRL) to minimize the long-term weighted cost including delay cost and bandwidth cost. DeMADRL is a model-free scheme based on Double Deep Q-Learning (DDQN) and can obtain the optimal computation offloading and bandwidth allocation decision-making policy by training the neural networks. The comprehensive simulation results show that the proposed DeMADRL optimization scheme has a nice convergence and outperforms the other three baseline algorithms.