Background: Biofortified orange-fleshed sweetpotato (OFSP) varieties are being promoted to reduce vitamin A deficiencies due to their higher beta-carotene content. For OFSP varieties to have impact they need to be accepted and consumed at scale amongst populations suffering from vitamin A deficiencies. Objective: We investigated the sensory and cultural acceptability of OFSP varieties amongst households with children aged between 2–5 years old in two areas in Central and Southern Malawi using an integrated model of the Theory of Planned Behavior (TPB) and the Health Belief Model (HBM). Methods: Sensory acceptability was measured using a triangle, preference and acceptance test using three OFSP varieties and one control variety, among 270 adults and 60 children. Based on a food ethnographic study, a questionnaire on cultural acceptability was developed and administered to 302 caretakers. Data were analyzed by calculating Spearman’s correlations between constructs and multiple linear regression modeling. Results: The sensory evaluation indicates that all three OFSP varieties are accepted (scores >3 on 5-point scale), but there is a preference for the control variety over the three OFSP varieties. Almost all caretakers are intending to frequently prepare OFSP for their child in future (97%). Based on regression analysis, the constructs ‘subjective norms’ (β = 0.25, p = 0.00) reflecting social pressure, and ‘attitudes toward behavior’ (β = 0.14 p = 0.01), reflecting the feelings towards serving their child OFSP, were the best predictors for caretakers’ behavior to prepare OFSP for their child. Conclusions: Our study shows that both sensory and cultural attributes can influence acceptability of varieties and consumption amongst households with children. Considering these attributes can improve the impact of biofortified crops in future programming, by reducing Vitamin A deficiencies through the intake of these nutrient-rich crops.