Based on the Collins integral formula, the analytical spectral equations of the propagation of Gaussian-Shell mode (GSM) beam through a chromatics aberrated fractional Fourier transform (FRFT) system are derived. By giving the example of Lohmann II system, the effect of chromatic aberration coefficient, FRFT order and the relative transverse coordinate on the normalized intensity distributions and relative spectral shift on exporting surface are analyzed numerically. It is shown that the relative spectral shift changes with the FRFT order. The value of chromatic aberration can affect the value of the relative spectrum shifting, the critical FRFT order, at which the spectral switch taking place, and the magnitude of the spectral jumping. The relative spectrum shift changes with FRFT, and there are differences of changing rules of that in systems with different FRFT order. In addition the normalized specteum and relative spectral shift change with the chromatic aberration coefficient and relative transverse coordinate as well.