Bridges are subject to large-amplitude vibrations, known as wind-induced vibrations, which can cause various problems in high winds. Flutter is the most serious vibration caused by self-excited force. In addition, long-span suspension bridges are flexible frames that are prone to large deformations. Many researchers have shown that flutter instability is affected by non-linear characteristics. In this paper, the equivalent linearisation method (ELM) is used to solve the flutter state of the nonlinear flutter system of a long-span suspension bridge with cubic torsional stiffness. By solving the equivalent linearisation equations, the wind speed of the critical flutter vibration was obtained, and the supercritical Hopf bifurcation and limit cycle oscillations (LCOs) were analysed.