A headlight comprising a supporting structure for a lamp unit, the headlight comprising: an outer lens; a housing having a front surface opening that is covered with the outer lens; multiple lamp units contained in a light chamber that is formed by the outer lens and the housing;; and an optical axis adjuster configured to adjust an optical axis by changing tilt of the lamp unit, wherein each lamp unit includes a light source, a projection lens, and a tubular lens holder, the light source being made of an LED, the projection lens configured to collect light from the light source, and the lens holder integrally joined to the projection lens at a front-side opening and integrated with the light source at a rear-side opening, characterized in that the headlight further comprises an extension disposed between the lamp unit and the outer lens; a circumferential edge part of the projection lens has a lens flange that is formed around the projection lens and that extends radially outward, the extension has for each lamp unit a lamp hole to which the projection lens is tightly fitted and also having an overlapping portion (10a, 31) that is a circumferential edge part of the lamp hole and that overlaps the circumferential edge part of the projection lens, the overlapping portion (10a, 31) of the extension forms a ring-shaped step part that covers the lens flange, the multiple lamp units each have the projection lens that is tightly fitted to one of the lamp holes, the overlapping portion (10a, 31) and the circumferential edge part of the projection lens are overlapped and joined together, thereby fixing the projection lens to the extension, and the extension and the lamp unit are configured to tilt integrally in adjusting the optical axis. an outer lens; a housing having a front surface opening that is covered with the outer lens; multiple lamp units contained in a light chamber that is formed by the outer lens and the housing;; and an optical axis adjuster configured to adjust an optical axis by changing tilt of the lamp unit, wherein each lamp unit includes a light source, a projection lens, and a tubular lens holder, the light source being made of an LED, the projection lens configured to collect light from the light source, and the lens holder integrally joined to the projection lens at a front-side opening and integrated with the light source at a rear-side opening, characterized in that the headlight further comprises an extension disposed between the lamp unit and the outer lens; a circumferential edge part of the projection lens has a lens flange that is formed around the projection lens and that extends radially outward, the extension has for each lamp unit a lamp hole to which the projection lens is tightly fitted and also having an overlapping portion (10a, 31) that is a circumferential edge part of the lamp hole and that overlaps the circumferential edge part of the projection lens, the overlapping portion (10a, 31) of the extension forms a ring-shaped step part that covers the lens flange, the multiple lamp units each have the projection lens that is tightly fitted to one of the lamp holes, the overlapping portion (10a, 31) and the circumferential edge part of the projection lens are overlapped and joined together, thereby fixing the projection lens to the extension, and the extension and the lamp unit are configured to tilt integrally in adjusting the optical axis.