This paper attempts to seek answer to the question why some regions being economically better-off are performing poorly in respect of maternal and child health outcomes compared with those which are otherwise (economically) worse-off than the former. Analysing the data obtained from two purposively selected upazilas (sub-district) in Bangladesh, it also tries to explore the factors responsible for better maternal and child health outcomes. This paper found that the impact of better health service delivery system is much stronger than that of growth and the other factors on health outcomes. It also found that ensuring “accountability” of the health service providers is a key factor to provide better health service delivery.