Quasar pairs, a special subclass of galaxy pairs, are valuable in the investigation of quasar interaction and clustering, the coevolution between the two quasars' host galaxies, and the growth of supermassive black holes, as well as the formation and evolution of galaxies overall. However, quasar pairs on kiloparsec scales are observationally rare. The scarcity of available samples hindered the deeper exploration and statistics of these objects. In this work, we apply an astrometric method to systematically search for quasar candidates within a transverse distance of 100kpc to known quasars in the Million Quasar Catalog. These candidates are Gaia sources with proper motions and parallaxes that are consistent with zero. A visual inspection of the sample was performed to remove the contamination of crowded stellar fields and nearby galaxies. A total of 4112 quasar pair candidates were isolated, with a median member separation of 8.81", a median Gaia G-band magnitude of 20.52, and a median redshift of 1.61. Following a comparison of our catalog with three major candidate quasar pair catalogs, we identified 3984 new quasar pair candidates that had previously been overlooked in the three catalogs. Several interesting quasar pair candidates are highlighted and discussed in this work. We also offer a brief discussion of our quasar selection and several techniques for improving the success rate of quasar pair selection. Extensive spectroscopic follow-up campaigns are currently underway to validate their astrophysical nature.