The spectroscopic sky survey carried out by the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) provides the largest stellar spectra library in the world to date. A large number of new DA white dwarfs had been identified based on the LAMOST spectra. The effective temperature (T-eff) and surface gravity (log g) of most DA white dwarfs were determined and published in the catalogs. We selected ZZ Ceti candidates from the published catalogs by considering whether their Teff are situated in the ZZ Ceti instability strip. The follow-up time-series photometric observations for the candidates were performed in 2015 and 2016. Four stars: LAMOST. J004628.31+343319.90, LAMOST. J062159.49+252335.9, LAMOST. J010302.46+433756.2, and LAMOST. J013033.90+273757.9 are finally confirmed to be new ZZ Ceti stars. They show dominant peaks with amplitudes rising above the 99.9% confidence level in the amplitude spectra. As LAMOST. J004628.31+343319.90 has an estimated mass of similar to 0.40 M circle dot, and LAMOST. J013033.90+273757.9 has a mass of similar to 0.45 M circle dot derived from their log g values, these two stars are inferred to be potential helium-core white dwarfs.