We report the first results of our systematic search for strongly lensedquasars using the spectroscopically confirmed quasars in the SloanDigital Sky Survey (SDSS). Among 46,420 quasars from the SDSS DataRelease 3 (~4188 deg2), we select a subsample of 22,683quasars that are located at redshifts between 0.6 and 2.2 and arebrighter than the Galactic extinction-corrected i-band magnitude of19.1. We identify 220 lens candidates from the quasar subsample, forwhich we conduct extensive and systematic follow-up observations inoptical and near-infrared wavebands, in order to construct a completelensed quasar sample at image separations between 1'' and 20'' and fluxratios of faint to bright lensed images larger than 10-0.5.We construct a statistical sample of 11 lensed quasars. Ten of these aregalaxy-scale lenses with small image separations (~ 1''-2'') and one isa large separation (15'') system which is produced by a massive clusterof galaxies, representing the first statistical sample of lensed quasarsincluding both galaxy- and cluster-scale lenses. The Data Release 3spectroscopic quasars contain an additional 11 lensed quasars outsidethe statistical sample.