Based on the fact that a hard aperture function can be expanded by an approximate sum of complex Gaussian functions with finite numbers, the approximate analytical expressions for the off-axial Hermite–cosh-Gaussian beams and off-axial cosh-Gaussian beams passing through an apertured paraxial ABCD optical system have been derived. By doing some numerical simulations the results obtained by the approximate analytical expression are compared with those obtained by the diffraction integral formula directly. It is shown that the former has good consistency with the latter and that our method can significantly improve the numerical calculation efficiency. The approximate analytical expressions for the kurtosis parameter and beam radius of an off-axial Hermite–cosh-Gaussian beam through an apertured paraxial ABCD optical system are also derived.