There is growing interest among the public in demography since demographic change has become the subject of political debates in many countries. Statistics on demography are used to support policy-making and monitor demographic behaviour of political, economic, social and cultural perspectives. Most studies have used descriptive statistics to study demographic characteristics. Moreover, most of these studies investigate effects of individual character at a time. Therefore, there is a need to come up with more robust statistical methods, such as predictive models for demographic studies. The objective of this study was to predict the effect of demographic characteristics on parity using Poisson regression model. Secondary data on parity, age, marital status and education level was collected from Chuka and Embu hospital maternal units from 2013 to 2017. The data was analysed using R-statistical software. Three Poisson regression models (PRMs) were fitted. The likelihood ratio test of all the Poisson regression models had p-values < 0.05 indicating that all the models were statistically significant. Deviance test and Akaike Information Criterion (AIC) were used to assess the fit of Poisson regression models. The overall Poisson model had residual deviance of 184.23, which was the lowest of all other fitted PRM models, suggesting that it was the best fit. The AIC of the PRM with both education and marital status as the predictors had the lowest AIC value of 2078.620, indicating that it was the best fitted model. The dispersion test proved that PRM was not over-dispersed, confirming the model as a good fit of the data. The improved model can be used in prediction of population growth rates.