This study aims to investigate the methods of solar and lunar eclipse prediction in China before the 4th century AD, with a detailed example of the eclipse theory in the Jing chu li (Luminous Inception System 景初暦). As the official calendar of the Jin dynasty and the Kingdom Wei during the Three Kingdoms period, the Jing chu li was used for more than 200 years after it was adopted in AD 237. Eclipse theory is important in Chinese calendrical systems not only because it reflects the mathematical astronomy at the time, but also for the significance of eclipses within Chinese judicial astrology. For example, solar eclipses were recognized as one of the most ominous astronomical phenomena. This paper will address two questions: first, when did Chinese astronomers start to predict solar and lunar eclipses? Second, how did ancient Chinese astronomers improve eclipse prediction methods from the San tong li (Triple Concordance System 三統曆) of the Western Han to the Jing chu li. Over this period, methods for predicting eclipses developed in three important ways: (i) from predicting only lunar eclipses to the prediction of both solar and lunar eclipses; (ii) from relying only on the mean periods of the sun and the moon to taking into consideration the variation in lunar velocity; (iii) from estimating only a rough date to predicting the eclipse’s magnitude and the direction of the eclipse shadow. In addition to a detailed analysis of the various calendrical systems, further evidence will be drawn from other texts including historical writings.