The statistical properties of partially polarized light in Gaussian stochastic plane wave fields have been studied. In this paper, the statistics of the stochastic plane electromagnetic （EM） wave fields with Weibull distributed is examined. The polarimetric Weibull_distributed wave is characterized by three parameters: the sum of the amplitudes of the two electric vector components, the angle which the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. The main properties of this important distribution are shown. Then the statistical properties of the normalized Stokes parameters are described in detail in Weibull_distributed stochastic fields. The joint and marginal probability density functions （PDF） of the three components of the normalized Stokes parameters are presented. Results of some numerical calculation are obtained. The description of the Weibull polarimetric wave field may be useful to random medium scattering and speckle filtering.