Abstract: Starting from the propagation equation of complex- argument cosh- Gaussian (ChG) beams passing through a paraxial ABCD optical system and based on the second- order moments method, the closed- form expression for the beam width of complex- argument ChG beams passing through a paraxial ABCD optical system is derived, the waist width and their location of the beams propagating in free space and through a thin lens are also deduced. Numerical calculations are made to illustrate the properties of the complex- argument ChG beams.