Multi-access edge computing (MEC) is an emerging technology of 5G and beyond mobile networks which deploys computation services at edge servers for reducing service delay. However, edge servers may have not enough computation capabilities to satisfy the delay requirement of services. Thus, heavy computation tasks need to be offloaded to other MEC servers. In this paper, we propose an offloading solution, called optimal delay offloading (ODO) solution, that can guarantee service delay requirements. Specificially, this method exploits an estimation of queuing delay among MEC servers to find a proper offloading server with the lowest service delay to offload the computation task. Simulation results have proved that the proposed ODO method outperforms the conventional methods, i.e., the non-offloading and the energy-efficient offloading [10] methods (up to 1.6 times) in terms of guaranteeing the service delay under a threshold.