Background Child mortality continue to be a major public health issue in most developing countries; albeit there has been a decline in global under-five deaths. The differences in child mortality can best be explained by socioeconomic and environmental inequalities among countries. In this study, we explore the effect of country-level development indicators on under-five mortality rates. Specifically, we examine potential spatio-temporal heterogeneity in the association between major world development indicators on under-five mortality, as well as, visualize the global differential time trend of under-five mortality rates. Methods The data from 195 countries were curated from the World Bank’s World Development Indicators (WDI) spanning from 2000 to 2017 and national estimates for under-five mortality from the UN Inter-agency Group for Child Mortality Estimation (UN IGME).We built parametric and non-parametric Bayesian space-time interaction models to examine the effect of development indicators on under-five mortality rates. We also used employed Bayesian spatio-temporal varying coefficient models to assess the spatial and temporal variations in the effect of development indicators on under-five mortality rates. Results In both parametric and non-parametric models, the results show indicators of good socioeconomic development were associated with a reduction in under-five mortality rates while poor indicators were associated with an increase in under-five mortality rates. For instance, the parametric model shows that gross domestic product (GDP) (β = − 1.26, [CI − 1.51; − 1.01]), current healthcare expenditure (β = − 0.40, [CI − 0.55; − 0.26]) and access to basic sanitation (β = − 0.03, [CI − 0.05; − 0.01]) were associated with a reduction under-five mortality. An increase in the proportion practising open defecation (β = 0.14, [CI 0.08; 0.20]) an increase under-five mortality rate. The result of the spatial components spatial variation in the effect of the development indicators on under-five mortality rates. The spatial patterns of the effect also change over time for some indicators, such as PM2.5. Conclusion The findings show that the burden of under-five mortality rates was considerably higher among sub-Saharan African countries and some southern Asian countries. The findings also reveal the trend in reduction in the sub-Saharan African region has been slower than the global trend.