This paper assessed the errors of the simulation for a stationary Gaussian multi-variate wind process, which is carried out by using the original spectral representation method (OSRM) or the proper orthogonal decomposition-based spectral representation method (PSRM). To begin with, a set of formulas which describe the two types of SRM as well as the close-form stochastic errors produced by them are presented in a standard form. Accordingly, the errors produced by the simulation of a 64-point simplified wind field using the PSRM and OSRM are computed and then compared in terms of relative global spectral stochastic errors and relative stochastic errors of standard deviations. It can be concluded from the numerical example that the errors produced by the PSRM are not only less in total but also distributed to every point more uniformly than the PSRM; thus the PSRM should be preferred to. In addition, the influence of the number of frequency steps on the errors is discussed in detail. Some approaches for relieving the errors are also suggested.