By using a computational procedure of three-dimensional aerostatic and aerodynamic stability analysis of long-span bridges, the dynamic characteristics, structural stability including the aerostatic and aerodynamic stability are firstly analyzed for a three-tower cable-stayed bridge with main spans of 1400 meters, the parametric analysis is then conducted, and finally a favorable structural scheme of the example bridge is proposed and confirmed numerically. The results show that long-span three-tower cable-stayed bridge has significant flexibility with less vertical and especially horizontal stiffness, and is sensitive to the transverse wind action; long-span three-tower cable-stayed bridge exhibits a coupled aerostatic instability mode of vertical bending and torsion; the aerodynamic stability is worse than the aerostatic stability for long-span three-tower cable-stayed bridge, the flutter critical wind speed is significantly reduced by the static wind action, and thus the aerostatic effect must be involved in the aerodynamic stability analysis; the best wind stability is obtained for the example bridge as 2 auxiliary piers are set in each side span and their centerline differs from the side piers by 0.4 times the side span length, the center-to-side tower height ratio is 1.3, the tower height-to-span ratio is 1/5, 4 pairs of crossing cables are set at midspan of main spans, and the girder depth is 5.0 m.