<p>Mobile edge computing provides task offloading services for users close to edge servers, greatly reducing the computing pressure of users, decreasing the energy consumption and delay of task to be offloaded. This paper studies the problem of minimizing the average energy consumption of task offloading based on the premise that data on wireless links has delay requirements and variable offloading rate. Firstly, by utilizing the random variation characteristics of wireless channel quality, a task offloading average energy consumption minimization problem based on variable offloading rate is constructed. Then, it is transformed into an optimal stopping rule problem and the existence of the optimal stopping rule is proved. Finally, the optimal offloading rate threshold based on variable offloading rate of the edge terminal at each channel detection time is obtained by solving the approximate optimal stopping rule, realizing the task offloading energy consumption optimization strategy based on variable offloading rate using the optimal stopping theory. In simulation, the strategy proposed in this paper is compared with those in related literature in terms of the average energy consumption, the average offloading ratio, and the average scheduling period. The results showed that the proposed strategy had lower average energy consumption and higher average offloading ratio, achieving good energy optimization effects.</p>