The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived. As a special case, the propagation equation of unapertured cosh Gaussian beams is derived. Numerical calculation examples are given for the focusing of cosh Gaussian beams by an aperture lens. A comparison is made, which has shown the advantage of this method and the results are in good agreement with those obtained by the straight forward integration of Collins formula.