In order to study the transformation properties of a Hermite-Laguerre-Gaussian (HLG) beam though a fractional Fourier transform (FRFT) system in detail， the analytical expressions for the intensity distribution of HLG beam on the FRFT plane are derived from Collins formula. By using the derived expressions,numerical calculation examples have been presented to illustrate its propagation properties. It is shown that apart from the mode indices m,n, the intensity distribution on the FRFT plane depends on the fractional order p and parameter α, the variation with fractional order p and α is periodic,with the periods of 2 and 2π respectively. Furthermore, the beam shape of HLG beam maintains invariable in FRFT plane.