To provide a headgear such as a cap or sun visor, eliminating the soil at the reverse side of a peak or brim and uncomfortable feeling or oppressive feeling at a forehead, also widening eyesight and enabling not to have unreasonableness on a line of looking.

This headgear K1 consisting of a headgear main body 1 and a peak 2 is provided by installing a step member 3 having an almost bow shape by horizontal view between the front half part side of lower end circumferential edge part of the headgear main body 1 and the inner circumferential edge part of the peak 2 so as to form an opposing angle α of the surface of the step member 3 and the standing upper part outer circumferential surface of the headgear main body 1 as an obtuse angle, and an opposing angle β of the reverse surface of the step member 3 and the reverse surface of the peak 2 as an obtuse angle, and on using the same, constituting so as to wear it by positioning the inner circumferential edge part of the reverse surface of the step member 3 at the hairline 5 of hair of the forehead 4 of a headgear user.