In order to study beam waist width and waist location of cosh-Gaussian beams in a Gradient-index medium, the propagation field of cosh-Gaussian beams in a gradient-index medium is deduced, and expressions of spot size , beam waist width and waist location by using the definitions of second-order moment are presented. Based on the expressions, the influence of the Gradient-index medium on the spot size, beam waist width and waist location are mainly discussed. The results show that spot size cyclical changes in a Gradient-index medium with increasing distance from the propagation, and the cycle is determined by gradientindex parameters. With increasing eccentric parameters, beam waist width first decreases then increases and stabilizes at last, and the spot size oscillation amplitude is determined by eccentric parameters.