As a novel wind-sensitive structure, the shape and dynamic characteristics of the cylindrical-cone steel structure cooling tower is complex, the structural flexibility and the wind-induced effect are significantly increased. Its overall stability is one of the key problems in structural analysis and design, especially the influence of structure geometry, material nonlinearity and high order mode. Firstly, CFD numerical simulation was used to obtain the wind load distribution model. Then, we established a finite element model of the integrated steel structure cooling tower with the main cylinder + stiffening truss + accessory truss (hinged). The buckling modes with different eigenvalues are used as the initial geometric defect distribution. As well as, based on the finite element method of geometric and material dual nonlinearities, we systematically researched the stability of the steel structure cooling tower under different wind speeds, which involves divergent instability, extreme instability, critical wind speed and static wind response. The results show that the critical buckling bearing capacity of steel structure cooling towers is reduced by considering the geometric and material dual nonlinearities. The fundamental buckling waveform is relatively small and is not sensitive to the initial geometric imperfections. With the increase of wind speed, the order of buckling occurs as auxiliary truss, reinforced truss and the main cylinder. The influence of geometric imperfection coefficient and the order number on buckling critical wind speed is small, but with the increase of order, nonlinear analysis in the process of deformation trend by affiliated truss gradually transferred to the main cylinder. The main conclusions can be used as a reference for the verification of wind stability of such new steel structure cooling towers.