The literature on public health shows that health status of children and their nutritional status influence their health and well-being in adulthood. Therefore, policies to improve the health status of a population must consider children’s health and take into account all the elements that can influence child health status. The inequality of opportunity (lack) and efforts (behaviour in relation to health) towards improvement of the health status and mortality of individuals raises the issue of unequal distribution of health in a given population. However, this subject is relatively less discussed in the literature on public health in developing countries, including Togo. By focusing on health inequalities of opportunity, we analyze their evolution and contribution to children’s health (as measured by the standardized height) in Togo using data from Demographic and Health Survey (DHS) 1998 and 2013. The objective of this study is to measure and compare the importance of the contribution of inequality of opportunity (from differences in life circumstances) to total health inequality of children under 5 years. Because children are not accountable for any part of their health outcomes by age five, total inequality is decomposed into a part due to inequality of opportunity (observed variables) and another part due to other unobserved factors (inequality within opportunities) after controlling for the inequality from random variations in the health status of children or genetic variations from a reference population (healthy population). The methodological approach is based on decomposable general entropy measures such as the Theil-T index to measure total inequality after dealing with natural variation in the height of children. This inequality is decomposed into within- opportunities inequality and the between-opportunity (inequality of opportunity) by using a non-parametric approach after building the opportunity groups with the selected circumstances variables. The results show that the total health inequality experienced a decline between 1998 and 2013 from 0.65 to 0.26 in 15 years. This decrease is also observed for the inequality of opportunity and in within opportunity. The contribution from inequality of opportunity (inter-group inequality of opportunity) has increased over the period 1998-2013. It increased from 0.14 to 0.18, respectively, in 1998 and 2013. These relatively low levels of inequality of opportunity are interpreted as an estimate of the lower bound of the set of variables in circumstances that may influence the children’s health. In view of the results, the increase in the level of inequality of health opportunities comes more from the increase in the contribution of the unfavourable opportunities group.