The variability sky survey is a very effective method of searching for quasars. In the paper, we present a novel method to discriminate quasars from variable stars based on their intrinsic variabilities. The power-law model is used to fit the light-curve structure function in five wavebands, but the value of the structure function is normalized. The developed method is applied to 1411 spectroscopically confirmed quasars and 174 stars in SDSS stripe 82. We set a suitable criterion, then obtain a reasonable classified result. The classification accuracies about quasars and stars reach 92.2% and 83.6% respectively. Compared with the structure function only based on one physical parameter, the normalized structure function with amplitude and power-law index has a good efficiency to deal with these data. The method for selecting quasar candidates ensures big sky survey telescope a high survey efficiency and saving valuable astronomical observation time. The results support that the optical variabilities of most of quasars originate from the instabilities of accretion disks.