The National Foundation Day of Korea (개천절, 開天節) is currently celebrated on October 3 in Gregorian calendar. We review the history of dating the National Foundation Day of Korea and make a suggestion that it be celebrated on October 3 in the lunar calendar. We present numerous historical records on heaven-worship rites supporting the date October 3 in the lunar calendar. It is pointed out that October 3 in the solar calendar has been adopted in 1949 by the National Assembly with the thought that the lunar calendar is inferior and behind the times. The thought originates from misunderstanding on the value of the lunar calendar and from the ignorance of importance of history and tradition. Since there are now many national holidays that follow the lunar calendar, the logic of the National Assembly in 1949 also makes no sense. We emphasize that the lunar calendar should be followed for the National Foundation Day of Korea for its historical and symbolic characteristics restoration. We also investigate the year of the foundation of the first country of Korea, Dangun Joseon. It is found that even though the majority of the literature before late 15th century recorded the beginning year of Dangun Joseon dynasty to be equal to that of Liao Dynasty (堯), it was accidentally changed to the 25th year of Liao Dynasty in 1484 through a misinterpretation of the previous records. We claim that the beginning year of Dangun Joseon should be set to that of Liao Dynasty as recorded in the original literature in the earlier days. According to the two main opinions accepted by Korea, the beginning year of Liao Dynasty was 2357 B.C. or 2333 B.C., which correspond to the year of Gap-Jin (the 41st year of the sexagenary cycle) or Mu-Jin (the 4th year of the sexagenary cycle), respectively.