Abstract: Based on the spectral analysis theory and the turbulent physical spectral tensor model, a stochastic harmonic function method is proposed for the simulation of 3-directional (3-D) fluctuating wind fields. The physical spectral tensor model proposed in the IEC code is firstly introduced based on the physical properties and the rapid distortion theory (RDT) of the 3-D atmospheric boundary layer turbulent field. Then, by introducing the stochastic harmonic function representation, the 3-D fluctuating field is expressed as the superposition of a series of harmonic functions modulated by the stochastic wavenumbers and phase angles. A two-step acceptance-rejection scheme is proposed to determine the representative point set of the stochastic wavenumbers. The zero-phase evolution time model is adopted to express the high-dimensional stochastic phase angles as the stochastic functions of 4-dimentional random variables. For the purpose of verification, the numerical examples of simulating the 3-D fluctuating wind field for a bridge tower are performed. It is demonstrated that the proposed method can simulate the 3-D fluctuating wind field corresponding to different turbulence modes with a small number of harmonic terms and fair accuracy.