Based on the unified theory of coherence and polarization of random electromagnetic beams and the propagation law of partially coherent light, the change in the degree of polarization of beams which is generated from a partially coherent source after passing through a series of circular apertures was investigated. Gaussian Schell-model beam was taken as an example to study the change in the degree of polarization for on-axial points. It is found that, with the increase of the number of circular apertures, the degree of polarization for on-axial points will change. It is shown that for a sufficiently long propagation distance, the degree of polarization for on-axial points will tend to a certain value. And three circular apertures are chosen as a typical multiple circular apertures system for investigating change in the degree of polarization. It is shown that, the change in the degree of polarization depends on the size of circular apertures, the distance between circular apertures, the correlation length in the source plane and the degree of polarization in the source plane.