A sunshade for use with a cap is made from a thin, tinted, resilient plastic sheet which is attached to the underside of a cap's visor by means of a duck-bill or semi-moon shaped support. The sunshade has an elongated minor segment and an elongated major segment with a seam or crease dividing the two segments. The major segment can be flipped downwardly to protect the eyes of the cap's wearer from the sun's rays. The seam or crease acts as a hinge between the minor and major segments.