In this paper, the analytical expressions for the total intensity, the on-axis spectrum and the degree of coherence of polychromatic partially coherent decentred laser beams propagating in non-Kolmogorov turbulence are derived. The influences of the beam decentred parameter β, the fractal constant α of the atmospheric power spectrum, and the bandwidth Ω of spectrum on propagation property are studied. It is shown that the larger the value of β, the bigger the deviation of centre of beam gravity from the propagation axiis, and the more unsymmetrical the coherence degree is. However, the on-axis spectrum is nearly independent of β. The influence of α on total intensity, on-axis spectrum and coherence degree is non-monotonic. When α=3.1, the propagation properties are most affected by turbulence. It is mentioned that at certain propagation distances, the shifts of on-axis spectrum are the same for different values of α. Furthermore, the on-axis spectral shift disappears at other propagation distances which are independent of Ω, and these propagation distances decrease due to turbulence. The results obtained in this paper will be useful for the applications of polychromatic partially coherent decentred laser beams propagating in non-Kolmogorov turbulence.