•A three-wave longitudinal design was applied to examine whether and how family SES affecting children’s academic achievement during school closure times.•Family SES could predict children’ later academic achievement above and beyond their prior academic achievement and other demographics.•Family SES influenced children’s later academic achievement through the chain-mediating effects of parental involvement and student engagement.•Neither parent involvement nor student involvement alone mediated the relationship between family SES and subsequent academic achievement. With a three-wave longitudinal design, the current study examined the impact of family socioeconomic status (SES) on parental involvement and student engagement in promoting children’s academic achievement during the coronavirus disease 2019 (COVID-19) pandemic. We recruited data from 246 mother–primary school student dyads, and the mean age of children at Wave 1 was 10.57 ± 0.97 years (range = 9–13 years). The academic achievement of these children was measured both before and after school closures. Family SES, parental involvement, and student engagement were assessed during the school closures. The results indicated that family SES could predict children’s later academic achievement after accounting for their prior academic achievement and other demographics (i.e., the significant total effect in the model). Moreover, parental involvement and student engagement played chain-mediating roles in the effect of family SES on children’s later academic achievement. Neither parent involvement nor student involvement alone mediated the relationships between family SES and subsequent academic achievement. Suggestions are provided to minimize the negative impact of low family SES on children’s academic achievement during pandemics.