For large-scale and highly mobile unmanned aerial vehicular networks(UAVNets), routes planning plays an important role in energy-efficient data transmission. Based on quantum annealing, we propose a routes planning algorithm to minimize the energy consumption. The simulation results by using the path integration Monte Carlo method show that in the same times of iteration, the quantum annealing algorithm can obtain better results than the simulated annealing algorithm, and the success rates are also greatly improved. Compared with the simulated annealing algorithm, the average energy consumption of the proposed algorithm is reduced by about 21%, and the reliability of the routes programming results is relatively higher according to the simulation results. Quantum annealing-based algorithm can also be used in other combinatorial optimization problem in information network.