We investigate the dynamics of partially coherent Pearcey–Gauss beams propagating in free space, theoretically and experimentally. They are produced by introducing the degree of coherence (DOC) function with Gaussian Schell-model correlation into the light source in the frequency domain. Under a nearly incoherent state, the oscillation of the sidelobe turns smooth, and the intensity distribution concentrates on the mainlobe. Particularly, partially coherent Pearcey–Gauss beams would maintain the inherent properties of autofocusing performance and inversion effect without diminishing the autofocusing distance and form-invariable propagation. Moreover, the opening angle and the shift of peak intensity of the beams can be controlled by the binary parabola in the spectrum distribution of the Pearcey function. Our experimental results are in great agreement with the theoretical analysis.