In a new release of the fourth Fermi Large Area Telescope source catalog (4FGL) in September a) , 5065 γ-ray sources are reported, including 3207 active galactic nuclei (AGNs), 239 pulsars, 190 other sources and 1429 unassociated sources. We employ two different supervised machine learning classifiers, combined with the direct observation parameters given by the 4FGL fits table b) , to search for sources potentially classified as AGNs and pulsars in the 1429 unassociated sources. In order to reduce the error caused by the large difference in the sizes of samples, we divide the classification process into two separate steps in order to identify the AGNs and the pulsars. First, we select the identified AGNs from all of the samples, and then select the identified pulsars from the remaining. Using the 4FGL sources associated or identified as AGNs, pulsars, and other sources with the features selected through the K-S test, we trained, optimized, and tested our classifier models. Then, the models are applied to classify the 1429 unassociated sources. According to the direct calculation results of the two classifiers, we show the sensitivity, specificity, accuracy in each step, and the class of unassociated sources given by each classifier. The accuracy obtained in the first step is approximately 95%; in the second step, the obtained overall accuracy is approximately 80%. Combining the results of the two classifiers, we predict that there are 674 AGN-type candidates, 86 pulsar-type candidates, 177 other types of γ-ray candidates, and 492 of uncertain type.