An eyeglass assembly having a secondary eyeglass frame combined with a main eyeglass frame by a protection strip is provided. A pair of eyeglass temples connected to the main eyeglass frame is adjustable to an angle as desired. When the eyeglasses are used for sport purpose, a strap may be fastened to the eyeglass temples by inserting a stopping portion of an engaging member of the strap into a preset hole on the eyeglass temple and allowing the stopping portion engaged with a crossed inner groove adjacent the hole by rotating at a direction such that the strap and the eyeglass temples can be quickly fastened to achieve stable positioning or quickly disassembled when not in use.