The total fertility rates in Taiwan area have been falling rapidly since 1960's, which reached a record low 1.4 in 2001, and trigger the population aging in Taiwan area. Possible causes attributing to this rapid decrease include more opportunities of higher education and employment for the female, which generally are treated as two of the main reasons for the delay of childbearing. However, the falling of fertility rates vary quite a lot in different age groups, and thus most well-known fertility models (such as Gamma and Lee-Carter models) fail to produce accurate predictions. In this paper, we shall extend the study of Huang and Yue (2002) and continue looking for acceptable fertility projection models. The models considered in this study include, in addition to traditional models for age-specific fertility rates, models for cohort fertility rate (CFR), age-and-parity specific birth rate, and diffusion. Data from 1949 to 1996 (or 1975 to 1996 for age-and-parity specific birth rate) are used as a pilot for verifying the model which has the best fit for data gathered from 1997 to 2001. We also consider the effect of Chinese zodiac to adjust the prediction values. We find that simpler models, such as individual group estimation, have smaller prediction errors comparing the complicated models such as the CFR model.