By using the Wigner distribution function(WDF)method,the fractional Fourier transform (FRFT) of beams is studied.HermiteGaussian (HG) beams are taken as an example; closedform expressions for the intensity distribution and beam widths of HG beams at the FRFT's plane are derived and changes in the intensity dist ribution of HG beams with the order of the FRFT are illustrated with numerical examples.It is shown that a symmetrical intensity distribution with equal beam width in the x and y directions can be achieved by a suitable choice of the transform order p.