The predicting of the Leonid meteor shower in history, especially during recent 20 years, has been expatiated and analyzed systematically, including the contribution of the author. The recent return of Comet 55P/Tempel-Tuttle in 1998 has push not only observational activities on the Leonid meteor shower, but also the research and verification about its prediction. Up to now, some predictions about maximum time of showers have shown very high veracity, and some predictions apparently have made mighty advantages in intensity of the shower. It seems these two kinds of method accentuate different aspects of the meteor swarm in 3-dimentional space. The combination of their success of different methods will make the predictions more maturate.