Sub-pc binary massive black holes(BBHs)are longly anticipated to exist in many QSOs but observationally elusive.In this paper,we propose a novel method to probe sub-pc BBHs/binary QSOs through the microlensing of lensed QSOs.If a QSO hosts a sub-pc BBH in its center,it is expected that the BBH is surrounded by a circum-binary disk at outside region,each component of the BBH is surrounded by a small accretion disk,and a gap opened by the small component in between the circumbinary disk and the two small disks.Assuming such a structure for BBH systems,we generate mock microlensing light curves for both BBH QSO systems and single massive black hole(MBH)QSO systems.We show that the microlensing light curves of a BBH QSO system at some given bands can be significantly different from that of a single MBH QSO system because of the existence of the gap and the rotation of the BBH and its associated small disks around the mass center.We extract the half-light radius of the emission region at different wavelengths from those mock light curves and find that the obtained half-light radius relations of BBH QSO systems can be much flatter than that of single MBH QSO systems at a wavelength range determined by the BBH parameters,such as the total mass,mass ratio,separation,etc.,which is primarily due to the existence of the gap.Such a unique feature of BBH QSO systems can be used to select and probe sub-pc BBHs in a large number of lensed QSOs that will be discovered by current and future big surveys,such as the Panoramic Survey Telescope and Rapid Response System(Pan-STARRS)and the Large Synoptic Survey telescope(LSST).