Based on several magnetic nonpotentiality parameters obtained from the vector photospheric active region magnetograms obtained with the Solar Magnetic Field Telescope at the Huairou Solar Observing Station over two solar cycles, a machine learning model has been constructed to predict the occurrence of flares in the corresponding active region within a certain time window. The Support Vector Classifier, a widely used general classifier, is applied to build and test the prediction models. Several classical verification measures are adopted to assess the quality of the predictions. We investigate different flare levels within various time windows, and thus it is possible to estimate the rough classes and erupting times of flares for particular active regions. Several combinations of predictors have been tested in the experiments. The True Skill Statistics are higher than 0.36 in 97% of cases and the Heidke Skill Scores range from 0.23 to 0.48. The predictors derived from longitudinal magnetic fields do perform well, however, they are less sensitive in predicting large flares. Employing the nonpotentiality predictors from vector fields improves the performance of predicting large flares of magnitude >=M5.0 and >=X1.0.