In the early Ming China, a Chinese-Islamic calendar, Huihui-lifa was compiled by a group of Chinese and Muslim astronomers. This early version of Huihui-lifa does not exist, but there are extant new versions of Huihui-lifa revised by Korean and Chinese astronomers in 1444 and 1477 under the name of Chiljeongsan Oepyeon and Qizheng Tuibu, respectively. These two version of Huihui-lifa include the Non-Ptolemaic star tables which give the longitudes, latitudes, and magnitudes of 277 stars in the ecliptic region. Interestingly, it is known that these star tables have a common origin with a star table in the Sanjufini zij of Tibet. This study, therefore, examines the epoch and precession rates of the star tables in the Chiljeongsan Oepyeon, Qizheng Tuibu and Sanjufini zij, and traces their origin and transmission route etc. In this work, we confirmed that the epoch and precession rate of star table in Sanjufini zij are vernal equinox of 1363 and 4′ per 5 lunar years, meanwhile those values of star table in the Huihui-lifa are winter solstice of 1390 and 4′ per 5 solar years. It shows that their precession rates are different despite of same origin. Unexpectedly, however, we find that their different precession rates came from the Chinese astronomer’s misunderstanding of the Hijra lunar year as the solar year.