Cap of bicycle headset with easy adjustable mounting bracket

A cap of a bicycle headset with an easy adjustable mounting bracket, with the mounting bracket used for engaging with an accessory comprising:

• a cap including a hole and a recess;
• a mounting bracket pivotally engaged with the cap and including a pivot and a bracket, with the pivot disposed in the recess of the cap and including an orifice, with the bracket pivotally engaged with the pivot and pivotal about the pivot;
• a fastener inserted into the orifice and the hole and engagable with a star nut of a bicycle headset;
• and
• a joining structure disposed on the bracket, with the joining structure providing a joining end with which an accessory is engagable;
• wherein the bicycle headset engaged in a steer tube includes the fastener positionable between a first engaging position in which the cap is rotatable about the fastener and the pivot is not tightly disposed in the recess and the bracket is pivotal to various pivoting positions with respect to the cap and a second engaging position in which the cap is fixedly positioned on the steer tube and the pivot is tightly disposed in the recess and the bracket is fixedly positioned at one of the pivoting positions.