An asymptotic lifetime growth model of height is introduced by modifying a fundamental growth model considering a relative measure of maturity. This model is compared with the Preece-Baines model and the Jolicoeur et al. model for 365 Japanese females collected in Hiroshima. The pooled residuals and the amount of the AIC can evaluate the goodness of fit to the longitudinal growth records. The proposed growth model is the best among three models from a viewpoint of the goodness of fit. Some special points of growth curve are characterized mathematically and the estimates of these points are compared with ones of other growth models. The larger the value of growth velocity at take-off is, the higher the final height is. An empirical Bayesian approach is applied to an asymptotic lifetime growth prediction of an insulin-dependent diabetes mellitus patient.