Abstract: The invention comprises a fray-resistant wick made up of an elongated fiber core with a web surrounding the core, and a jacket surrounding the web. The web has a lower melting point than both the core and the jacket, with the web and jacket fusibly or adhesively bonded to the core to form an integral structure. The core or jacket may comprise a fiber glass yarn, and the web a thermoplastic resin such as polypropylene. The method of making the fray-resistant wick comprises forming an enlongated core of the fiber material and surrounding the core with the web, and then surrounding the web with the jacket. Heating the core, web and jacket to a sufficiently high temperature fuses the core and jacket to the web, thereby forming an integral wick structure. In an alternative embodiment, the method comprises surrounding the core with a web of adhesive material for the purpose of bonding the core and jacket.