Variable stars play a key role in understanding the Milky Way and the universe. The era of astronomical big data presents new challenges for quick identification of interesting and important variable stars. Accurately estimating the periods is the most important step to distinguish different types of variable stars. Here, we propose a new method of determining the variability periods. By combining the statistical parameters of the light curves, the colors of the variables, the window function and the Generalized Lomb-Scargle (GLS) algorithm, the aperiodic variables are excluded and the periodic variables are divided into eclipsing binaries and NEB variables (other types of periodic variable stars other than eclipsing binaries), the periods of the two main types of variables are derived. We construct a random forest classifier based on 241,154 periodic variables from the ASAS-SN and OGLE data sets of variables. The random forest classifier is trained on 17 features, among which 11 are extracted from the light curves and 6 are from the Gaia Early DR3, ALLWISE, and 2MASS catalogs. The variables are classified into 7 superclasses and 17 subclasses. In comparison with the ASAS-SN and OGLE catalogs, the classification accuracy is generally above approximately 82% and the period accuracy is 70%–99%. To further test the reliability of the new method and classifier, we compare our results with the results of Chen et al. for ZTF DR2. The classification accuracy is generally above 70%. The period accuracy of the EW and SR variables is∼ 50% and 53%, respectively. And the period accuracy of other types of variables is 65%–98%.