Fertility rate is one of the most important global indexes. Past researchers found models which fit to age-specific fertility rates. For example, mixture probability density functions have been proposed for situations with bi-modal fertility patterns. This model is less useful for unimodal age-specific fertility rate patterns, so a model based on skew-symmetric (skew-normal) pdf was proposed by Mazzuco and Scarpa (2011) which was flexible for unimodal and bimodal fertility patterns. In this paper, we introduce skew-logistic probability density function as a better model: its residuals are less than those of the skew-normal model and it can more precisely estimate the parameters of the model.