Adverse space-weather effects can often be traced to solar flares, the prediction of which has drawn significant research interests. The Helioseismic and Magnetic Imager (HMI) produces full-disk vector magnetograms with continuous high cadence, while flare prediction efforts utilizing this unprecedented data source are still limited. Here we report results of flare prediction using physical parameters provided by the Space-weather HMI Active Region Patches (SHARP) and related data products. We survey X-ray flares that occurred from 2010 May to 2016 December and categorize their source regions into four classes (B, C, M, and X) according to the maximum GOES magnitude of flares they generated. We then retrieve SHARP-related parameters for each selected region at the beginning of its flare date to build a database. Finally, we train a machine-learning algorithm, called random forest (RF), to predict the occurrence of a certain class of flares in a given active region within 24 hr, evaluate the classifier performance using the 10-fold cross-validation scheme, and characterize the results using standard performance metrics. Compared to previous works, our experiments indicate that using the HMI parameters and RF is a valid method for flare forecasting with fairly reasonable prediction performance. To our knowledge, this is the first time that RF has been used to make multiclass predictions of solar flares. We also find that the total unsigned quantities of vertical current, current helicity, and flux near the polarity inversion line are among the most important parameters for classifying flaring regions into different classes.