Abstract Because of extreme sensitivity to time and energy consumption, many computation‐ and data‐intensive tasks are difficult to implement on mobile terminals and cannot meet the needs of the rapid development of mobile networks. To solve this problem, mobile edge computing (MEC) appears to be a promising solution. In this study, we propose two offloading schemes in the multiple unmanned aerial vehicles (UAVs) enabled MEC network. Their optimisation goals are to minimise the global computing time and energy consumption of all UAVs, respectively. Different from previous research, the UAV can perform tasks locally or offload an appropriate percentage to the desired MEC server in the two proposed schemes. In order to get the minimum global computing time, we prove the existence condition and obtain the optimal offloading proportion. In addition, in order to minimise global energy consumption, we also obtain the optimal offloading proportion and present the optimal transmission power through solving Karush–Kuhn–Tucker conditions. Finally, because UAVs are selfish, we adopt the game theory to get optimal solutions of the proposed offloading strategies. Numerical results verify that the proposed schemes can effectively decrease the global computing time and energy consumption, especially for a large number of UAVs.