Since the study of non-Gaussian characteristics on wind pressures is conducted mainly through wind tunnel test data, field measurement results are very limited. However, these results provide the most direct data to master wind field characteristics. Therefore, field measurements of wind pressures on a rectangular structure are implemented, and the effective non-Gaussian wind pressure data are acquired and analyzed using the probability density distribution, the characteristic statistical parameters, and the correlations, respectively. The fluctuating wind pressures on the windward and non-windward surfaces of the rectangular structure show different degrees of non-Gaussian characteristics. Fluctuating wind pressures on the non-windward surfaces show relatively strong non-Gaussian characteristics with a negative bias, while those on windward surfaces display relatively weak non-Gaussian characteristics with either a negative or positive bias. The correlations on the windward surfaces are greater than those on the nonwindward surfaces, and there exists a phase angle of the non-Gaussian fluctuating wind pressures between the different measuring points in a horizontal orientation. Finally, a power spectral density function of non-Gaussian fluctuating wind pressures is established by fitting the autoregressive (AR) spectral estimation with the linear prediction error minimization. The results show that the fitting parameter is related to peak frequency depending on the non-Gaussian strength.