A low cost, easy to manufacture scent-dispersing mat apparatus has a flexible closed cell foam mat containing a plurality of blind holes extending from its upper surface. These blind holes are partially filled with a fragrant liquid scent, creating air spaces thereabove. The upper surface of the flexible closed cell foam mat is sealed with a polymeric sheet that entraps the air spaces in the blind holes, causing entrapped air to become saturated with fragrant scent vapor. The polymeric sheet is perforated by one or more fine needles at the blind hole locations. The perforations permit escape of fragrant scent-saturated air to the ambient when pressure is applied to the top surface of the mat. Upon release of pressure, the foam mat and the blind holes recover their shape; the entrapped air pressure decreases, drawing fresh ambient air into the entrapped air spaces.