The dynamic characteristics of bridge structures are important in wind stability analysis, seismic design, fatigue assessment, health inspection, and maintenance of bridge structures; however, the mechanical and dynamic properties of different bridge types are different. A long-span cable-stayed bridge has the advantages of large flexibility, long natural vibration period, low natural frequency, dense spectrum, and denser modal than those of general structures. In this paper, the dynamic characteristics of a cable-stayed bridge with single pylon and single cable plane in the maximum cantilever stage and the complete bridge are analyzed. The single-tower cable-stayed bridge has some unique characteristics, such as lower cost, and a more beautiful appearance, but its torsional rigidity is lower, which increases the risk of wind damage and earthquake damage. Therefore, a finite element analysis of this bridge in the maximum cantilever state is carried out, and the influences of the main components’ rigidity, the inclination angles of the stayed cables, the supporting conditions, and the locations of the auxiliary piers are analyzed for the sustainability of this type of cable-stayed bridge. The analysis results show that a cable-stayed bridge with single pylon and single cable plane has more flexibility, and that the lateral rigidity and torsional rigidity are smaller. Structure rigidity, dip angles of the stayed cables, and positions of the auxiliary piers all have significant influences on the dynamic characteristics of cable-stayed bridges.