In many applications, resource-aware devices are connected through a network, such as in the Internet of Things and energy hubs. These devices require proper coordination to achieve a high performance without violation of their resource limits. In this paper, we propose an asynchronous resource-aware multi-agent model predictive control to cooperatively coordinate agents to conduct a common task, whose resource concern is handled by a self-triggered control scheme. The consistency and recursive feasibility of the proposed MPC scheme are investigated. A reliable numerical implementation is introduced to deal with non-constant sampling times among agents, which is subsequently validated by a numerical example.