A cover (30) for covering the exterior of a through-wall air-conditioner installation in a building. A sheet of material has a shape that provides a rectangular outer wall (32) for covering a rectangular outer face of the through-wall air-conditioner installation and four sides (34, 36, 38, 40) that are folded inward for covering respective sides of the installation and joined at their ends to form four distinct corners for fitting to four corners of the installation. A hem (62) runs along the inner edge margins of the sides and encloses an elastic cord (60) that elongates to a stretched condition to allow the cover to fit over the exterior end of the installation for placing the sides in overlapping relation to the sides of the installation and that exerts a holding force for holding the hem against the four sides of the installation.