This paper investigates the effect of the epidemic of COVID-19 on under-five mortality in four Health and Demographic Surveillance Systems (HDDS): Siaya-HDSS in Kenya, Basse-HDSS in the Gambia, Niakhar-HDSS in Senegal, and Matlab-HDSS in Bangladesh. Inasmuch as the number of deaths due to COVID-19 is dependent on testing coverage, variations in case definitions, or the performance of health facility-based surveillance, the effect of COVID-19 on under-five mortality is estimated to be indirect, through a measure of excess mortality. We calculate the excess of mortality as the difference between the probabilities of dying in a calendar month affected by the pandemic and a counterfactual estimate that only depends on the secular trend in mortality of each site before the outbreak of COVID-19. We approach to this aim by forecasting the life tables of under-five mortality and quantifying the effects of the epidemic of COVID-19 on the most relevant indicators of mortality from zero to five years (e.g., the neonatal mortality, the post-neonatal mortality, the infant mortality rate, the child mortality rate, and the under-five mortality rate). Preliminary results did not identify any evidence of excess mortality that can be attributed to the COVID-19 outbreak, and these findings would contradict the predictions of earlier simulation studies.