This study examines the relationship between government health expenditure and health outcome in Nigeria using time series data on infant mortality, government health expenditure, school enrollment ratio and the gross domestic product for the period covering 1981 to 2020. The study sourced data from the World Bank data base and Central Bank of Nigeria (CBN) statistical bulletin. Infant mortality rate was used as a proxy for health outcome based on data availability and the literature. As dictated by the data, the study used Vector Autoregressive model (VAR) to analyse the relationship between government health expenditure and health outcome in Nigeria for the period under study. The variables in the model were all integrated of order one and were cointegrated using the Johansen’s cointegration test. Government health expenditure is found to have a negative relationship with infant mortality in Nigeria; an indication that an increase in health expenditure has the tendency to decrease infant mortality in Nigeria. The study finds school enrollment to be significant. Therefore, the study recommends among other things that government expenditure should be increased to diminish infant mortality as well as enhance school enrolment.