Health expenditure, child mortality and economic growth in Nigeria was examined using time series data covering the 1980 – 2020 sample periods. The Ordinary Least Square (OLS) technique was employed in analyzing the data. Empirical results showed a negative and insignificant impact of government health expenditure on under-five child mortality. It was also found that government capital expenditure had a negative and insignificant impact on under-five mortality, while government recurrent expenditure had a negative and significant impact on under-five mortality. Gross fixed capital formation had a positive and significant impact on under-five child mortality. It was also found that child mortality, government capital expenditure and domestic investment had a positive and significant impact on economic growth, while inflation had a negative and significant impact on economic growth. We recommend an increase in the yearly budgetary allocation to the health sector. However, the key to good outcomes is dependent not on the only mere increase in budgetary allocation but rather on implementing a public finance system that is good enough to extend and possibly link particular expenditure and revenue decisions and ensure appropriate usage of the allocated fund as transparently as possible.