Abstract: The simulation of fluctuating wind speed field is of a great significance, considering that the wind load is critical or even dominating for the safe design of large-sized engineering structures such as high-rise buildings, long-span bridges and megawatt wind turbines. The spectral representation method (SRM) is a kind of widely used simulation technique at present, which has to, however, deal with the challenge of unbearable computational efforts owing to the Cholesky decomposition or proper orthogonal decomposition (POD) at each discretized frequency with respect to the cross-power spectrum density (PSD) matrix. The wavenumber-frequency joint power spectrum and evolutionary wavenumber-frequency joint power spectrum based SRM were proposed recently, allowing an effective simulation of a homogeneous or nonhomogeneous wind field without Cholesky decomposition or POD. Further, the FFT technique can be utilized to improve the simulation efficiency when the spatial simulation points are evenly distributed. However, in the case of unevenly-distributed spatial simulation points, the FFT technique cannot be adopted. Thus, the simulation efficiency still needs to be enhanced. In order to reduce the computational costs resulted from the twofold summation over a frequency-wavenumber domain, the uneven discretization strategies, including structured method and acceptance-rejection method, are suggested in the present paper. The numerical examples of simulation in nonhomogeneous fluctuating wind speed fields in one-dimensional space for a bridge tower are performed, demonstrating the effectiveness of the proposed method.