Mobile edge computing (MEC) has been widely used in many scenarios due to its advantages such as low latency, high bandwidth, and strong real-time performance. For mobile edge computing in networks with multiple mobile users and multiple MEC servers, this paper proposes an adaptive delay-limited offloading scheme based on a multi-round auction model. First, a multi-round auction model is adopted. Users and servers select each other to achieve a globally optimal match. The proposed evaluation function is based on the delay and energy consumption that can be reduced by offloading, and weights the two parts based on the user’s optimization needs. At the same time, a mechanism for adaptive delay limitation is proposed. The threshold is dynamically updated according to the unloading feedback, which makes the algorithm dynamically adapt to the load changes in the network. Experimental results show that the proposed offloading scheme has obvious advantages in reducing the total delay and the total energy consumption of the system, effectively improving the system performance.