The partially coherent cos-Gaussian (CsG) beam was introduced.Analytical expressions for the propagation of partially coherent CsG beams through a paraxial ABCD optical system and the M2 factor were derived.Propagation properties of partially coherent CsG beams through an astigmatic lens were studied.It is shown that the M2 factor of partially coherent CsG beams is dependent on the spatial coherence parameter and the decentered parameter of partially coherent CsG beams,but independent of the astigmatic coefficient of the lens.The Gaussian-like,flat-topped,and dark-hollow different intensity profiles at the geometrical focal plane couldn be achieved by a suitable choice of the spatial coherence parameter,decentered parameter or astigmatic coefficient.Thus,the spatial shaping of partially coherent CsG beams is realizable.