We have investigated the feasibilities and accuracies of the identifications of RR Lyrae stars and quasars from the simulated data of the Multi-channel Photometric Survey Telescope (Mephisto) W Survey. Based on the variable sources light curve libraries from the Sloan Digital Sky Survey (SDSS) Stripe 82 data and the observation history simulation from the Mephisto-W Survey Scheduler, we have simulated the uvgriz multi-band light curves of RR Lyrae stars, quasars and other variable sources for the first year observation of Mephisto W Survey. We have applied the ensemble machine learning algorithm Random Forest Classifier (RFC) to identify RR Lyrae stars and quasars, respectively. We build training and test samples and extract ~ 150 features from the simulated light curves and train two RFCs respectively for the RR Lyrae star and quasar classification. We find that, our RFCs are able to select the RR Lyrae stars and quasars with remarkably high precision and completeness, with purity = 95.4% and completeness = 96.9% for the RR Lyrae RFC and purity = 91.4% and completeness = 90.2% for the quasar RFC. We have also derived relative importances of the extracted features utilized to classify RR Lyrae stars and quasars.