Based on the flat-topped beam model proposed by Li and the partially coherent light theory, the spectral propagating expression of the partially coherent flat-topped beam is derived, and its variation of spectral properties is studied quantitatively in the free space. The variation rule of the on-axis spectrum of the flat-topped light beam for different orders in the propagating process is analyzed in detail. The effects of the source's spectrum width and the spatial coherence parameter on the spectral properties are discussed. It shows that when the partially coherent flat-topped beam propagates in the free space, the light source parameters have more effects on the value of the relative frequency shift than on the total change trend of the spectrum along the propagation distance, which is primarily determined by the order of flat-topped beam.