Plastic visors such as are employed to reduce glare are customarily attached along one edge to a fabric or plastic head-encircling band and since the edge of the visor is exposed, it can cause considerable discomfort. It is, accordingly, an object of this invention to provide a headband designed to receive the rigid edge of the visor where the latter is attached thereto which will conceal and cushion the edge. The structure as thus made avoids the use of multiple parts which require assembling and stitching and is particularly well adapted to be incorporated in a conventional cap or hat where a visor is desirable wherein it will serve the double purpose of a support for attachment to the body of the cap or hat and for a sweatband as well as for an attachment of the visor thereto. Still another advantage derived from the fact that it can be manufactured inexpensively is that the plastic visor provides an ideal means for displaying emblems, logos and the like which make it attractive as a giveaway item for advertising purposes.