The wind-borne Pterocarya stenoptera seeds depend on their double wings to keep stable autorotation and long endurance in the wind. Their superior flight modes can be applied to biomimetic aircraft. For biomimetic aircraft, floating ability is one of the most important performances, which is mainly affected by the aerodynamic shape. Based on the shape of a natural Pterocarya stenoptera seed, aerodynamic optimization is carried out for biomimetic aircraft. To increase the optimization efficiency, machine learning method is used in the optimization framework. Firstly, an aerodynamic surrogate model based on the radial basis function neural network and numerical simulated dataset is developed for the biomimetic aircraft, which has an accuracy of 98.4% and 94.7% for lift and aerodynamic efficiency factor, respectively. Aerodynamic optimization based on the multi-island genetic algorithm is carried out, and an optimized shape is obtained for the biomimetic aircraft. Compared with the original shape, the aerodynamic efficiency factor of the optimized one has been increased by over 50%. The larger pressure difference between the windward side and leeward side of the wings and the larger leading- edge vertex contribute to a higher lift for optimized shape.