Neonatal (NMR), infant (IMR) and under-five (U5M) mortality rates remain high in Nigeria. Evidence-based knowledge of trends and drivers of child mortality will aid proper interventions needed to combat the menace. Therefore, this study assessed the trends and drivers of NMR, IMR, and U5M over a decade in Nigeria. A nationally representative data from three consecutive Nigeria Demographic and Household Surveys (NDHS) was used. A total of 66,158 live births within the five years preceding the 2003 (6029), 2008 (28647) and 2013 (31482) NDHS were included in the analyses. NMR was computed using proportions while IMR and U5 were computed using life table techniques embedded in Stata version 12. Probit regression model and its associated marginal effects were used to identify the predisposing factors to NMR, IMR, and U5M. The NMR, IMR, and U5M per 1000 live births in 2003, 2008 and 2013 were 52, 41, 39; 100, 75, 69; and 201, 157, 128 respectively. The NMR, IMR, and U5M were consistently lower among children whose mothers were younger, living in rural areas and from richer households. Generally, the probability of neonate death in 2003, 2008 and 2013 were 0.049, 0.039 and 0.038 respectively, the probability of infant death was 0.093, 0.071 and 0.064 while the probability of under-five death was 0.140, 0.112 and 0.092 for the respective survey years. While adjusting for other variables, the likelihood of infant and under-five deaths was significantly reduced across the survey years. Maternal age, mothers’ education, place of residence, child’s sex, birth interval, weight at birth, skill of birth attendant, delivery by caesarean operation or not significantly influenced NMR, IMR, and U5M. The NMR, IMR, and U5M in Nigeria reduced over the studied period. Multi-sectoral interventions targeted towards the identified drivers should be instituted to improve child survival.