A variable headlamp apparatus for a vehicle is capable of realizing various lighting functions by switching positions of the plurality of optical units only with a single drive unit. The variable headlamp apparatus includes: an optical unit having an emitter to emit light; a guide unit installed with the optical unit to guide a position of the optical unit to a fixed path; a link unit connected to the optical unit and including multiple links rotatably connected to each other to change the position of the optical unit; and a drive unit to rotate the links. In particular, the optical unit moves along the fixed path of the guide unit while switching a light irradiation direction of the emitter.