Many wake-oscillator models applied to study vortex-induced vibration (VIV) are assumed to be excited by ideal wind that is assumed to be uniform flow with constant velocity. However, in the field of wind engineering, the real wind is generally described as being composed of mean wind and fluctuating wind. A wake-oscillator excited by fluctuating wind should be treated as a randomly excited and dissipated multi-degree-of-freedom (DOF) nonlinear system. The study of such a system is challenging and so far there is no exact solution available. The present paper aims to carry out the study on the stochastic dynamics of VIV. The stochastic averaging method of quasi-integrable Hamiltonian systems under wideband random excitation is applied to study both the original Hartlen–Currie wake-oscillator model and a modified version excited by fluctuating wind. The probability and statistics of the random response of wake-oscillator in resonant (lock-in) case and in non-resonant case are analytically obtained, and the analytical results are confirmed using numerical simulation of the original system.