The analytical formulae of the beam width and the intensity distribution for fractional Fourier transform (FRFT) of cosh-Gaussian (ChG) beams are derived based on the characteristic of the equality between the rotation of the Wigner distribution function (WDF) and the FRFT. By using the derived formulae, the influences of the fractional order and the decentered parameter on the transformation properties of ChG beams in the fractional Fourier plane are studied in detail. Numerical calculation examples have been presented to illustrate the propagation properties of ChG beams through FRFT optical system. It was shown that for given decentered parameter, a flatted beams can be obtained by FRFT with suitable order. The derived formulae provide a simple and convenient way to study the FRFT of ChG beams.