We have analyzed the comet records in the Korean history books: Samguksagi, Goryeosa, and Joseonwangjosillok. For a comparison, the Chinese and Japanese comet records collected by Kronk (1999) have also been analyzed. Power spectrum of the time series of the comet records is used to find periodic comets. Statistically significant periodicities in the power spectrum are detected at the periods of 38-40 years, about 76 years, and 300-400 years for all Korean, Chinese, and Japanese comet records. We have also calculated the past orbits of some comets that have been recently observed, to check whether or not they were recorded in the history books. We use a multistep method to numerically integrate the comet's orbital motion backward in time to 51 B.C. The gravitational force due to the Sun and the nine planets, non-gravitational force, and the relativistic effects have been considered. Comparison of comet's perihelion passage time and the position on the sky with the historical records shows that the comet Halley were recorded at every passage in both Goryeo and Joseon periods. The orbital motion of the comet Pons-Brooks has also been compared with the Korean records. For the comet Tempel-Tuttle, Swift-Tuttle, and Ikeya-Zhang, we have compared our calculation of the orbital motions with those of the previous studies.