This paper identifies some major drivers of per capita public health expenditure growth in Tanzania using nationally representative annual data between 1995 and 2014. It used Bayesian model based on Markov Chain Monte Carlo (MCMC) simulation. The empirical result shows that both the real GDP per capita and population age 65 years and older exert a positive effect on per capita public health expenditure growth in Tanzania. Advances in medical technologies represented by life expectancy seem to reduce real per capita public health expenditure growth in Tanzania. However, the credible intervals for life expectancy and population age 65 years and older are very wide suggesting a lot of uncertainty with these estimates. The results imply that, future trends in per capita public health spending would mainly depend on the development of the economy such as real per capita gross domestic product. The result suggests the rapid growth in real per capita public health expenditure is likely to continue in future when the country economy becomes more robust and increase of population age 65 years and above.