Cable-stayed bridge with single cable plane has advantages in wide field of view. However, the problem of stability becomes especially important, because it can’t provide torsional stiffness. Based on LanQi SongHua River Bridge, a concrete cable-stayed bridge with single cable plane, the dynamic character, wind-resistant stability and flutter instability are analyzed, especially the analysis of the flutter stability at maximum double cantilever stage during construction phase. The paper analyzes the dynamic characters of the finite element model of the whole bridge through response spectrum method to reap the natural frequency, the vibration modes and other parameters, then checking the flutter stability. The results show that the bridge is very safe either at maximum double cantilever stage or finished stage. The analysis method provides a basis and references for the wind-resistant of cable-stayed bridge with single cable plane.