The short exposure and high precision photometry of TESS (Transiting Exoplanet survey satellite) space satellite provide good data for distinguishing variable stars and searching planets. In this paper, a series of methods, such as periodic spectrum and phase folding, are used to analyze 19995 target sources with high-quality variable data in TESS sector21, and these sources are classified. A total of 4624 variable stars are obtained, including 322 binary stars, 470 pulsating variables and 37 planetary transients. A total of 625 variable sources were cross matched with VSX (The International Variable Star Index). Among them, 131 were eclipsing binary systems and 31 were pulsating variables, whose periods are obtained by periodic spectrum. The other 59 variable stars have flare phenomena and 8 stars have transiting planets, whose rotation periods are also obtained through the periodic spectrum. The feasibility of the analysis of variable stars by TESS space satellite data is verified. By comparing the period results obtained by TESS space satellite sector21 with the variable star period provided by VSX variable star table, we found that the periods of most variable stars are consistent with those in this paper, and a few of them need to be corrected. Finally, the verified and corrected variable star tables are provided in this paper.