The partially polarized Gaussian Shell-model (PGSM) beam is proposed to describe the stochastic electromagnetic beam, and the array beam characteristics of PGSM beams combination are studied by means of Wigner distribution function (WDF). The analytical propagation equation of the array beams through a paraxial optical ABCD system is derived on the basis of the WDF. The intensity-moments characterization of the array beams is performed, and the important beam characteristic parameters such as the beam propagation factor (M2), beam width, far-field divergence angle and kurtosis parameter K of the array beams are expressed in a closed form. It is found that a flat-topped light-intensity profile can be obtained at a certain plane by a suitable choice of the beam number N, normalized separation, and also the coherence parameter of PGSM beams. The degree of polarization P of the array beams is no longer uniform upon propagation, it also changes additionally with normalized separation x′d.