Except in the U.S., the total fertility rates of developed countries have been smaller than the replacement level of 2.1. Without exception, the total fertility rates in Taiwan dropped to a historic low (1.2) in 2004 and are expected to be even smaller in 2006. In this study, we used the fertility data of four developed countries, Taiwan, Japan, the Netherlands and the USA (representing countries in Asia, Europe, and America), to fit the frequently used models (Gamma, Lee-Carter, Principal Component Analysis, Age-Group Fertility Rate, and Diffusion models) and determine which model has the best fit. We found that, for the total fertility rates, the best model in Taiwan, Japan, and the USA is our modified diffusion model, while in the Netherlands it is the age-group fertility rate model. For the age-specific fertility rates, the best model in Taiwan, Japan, and the Netherlands is the modified diffusion model, while in the USA it is the age-group fertility rate model. In addition, we use computer simulation to check the relative stability and relative efficiency of these fertility models. The age-group fertility rate model and the modified diffusion model also outperform other models. In conclusion, we recommend the readers use these two models.