This study measures the efficiency of health expenditures in improving child mortality outcomes, one of the targets of the Sustainable Development Goals (SDG). Bootstrap data envelopment analysis was used to evaluate the efficiency of 127 low- and middle-income countries (LMICs) from 2010 to 2019. We found that 45 percent of the LMICs operated at decreasing returns to scale (DRS), implying that an increase in inputs could generate only a smaller increase in health outcomes, whereas 53 percent exhibited increasing returns to scale, indicating that an increase in health expenditure could lead to a greater increase in health outcomes. The findings of the study also have greater policy implications. It suggests that countries which perform at DRS could deliberate on reallocating resources to improve their health outcomes since these countries May not benefit from an increase in the input level as their output will not increase at the same rate. Therefore, governments should focus on improving efficiency rather than increasing health expenditure, thereby enabling the achievement of the SDG target.