Childbearing is an essential event in woman’s life when she neglects her education and career for motherhood. The main cause of population growth in Nigeria is teenage childbearing as reported by many researchers with no significant intervention to reduce this menace. This work is designed to compare the results of Cox, Gompertz and Weibull models with a view to determine the model that best fits the data. To evaluate the effect of some risk factors on the hazard of teenage childbirth among Nigerian women, data obtained from National Demographic Health Survey 2013 was analysed. Results of the analysis showed that having a child at teen age depends on geopolitical zone, location, educational level, circumcision, household wealth index, religion belief, use of contraceptive, whether had a terminated pregnancy, forced sexual acts, awareness of HIV/AIDS, STI and the age of first sexual acts. Akaike Information Criterion (AIC) was employed to evaluate performances of the three models. Weibull regression model has the minimum AIC value compared to both Gompertz and Cox regression models. This shows that Weibull regression model provides best fit to the data.