Beam quality changes of Gaussian Schell-model (GSM) beams propagating through axicons are investigated in detail. The expressions showing beam quality changes of GSM beams are derived in terms of Wigner distribution function. It is shown that, when a GSM beam passes through a divergent or convergent axicon, the beam quality factor (M2 factor) becomes larger. The increment of the M2 factor is dependent on the incident beam size, wave number, refractive index of the axicon material and the angle of the axicon; but it is independent of the coherence of the beam. The explanation for the increment of the M2 factor is also given.