A heightened hedonic response to sweet tastes has been associated with increased alcohol preference and alcohol consumption in both humans and animals. The principal goal of this study was to examine blood oxygenation level dependent (BOLD) activation to high- and low-concentration sweet solutions in subjects who are either positive (FHP) or negative (FHN) for a family history of alcoholism. Seventy-four non-treatment seeking, community-recruited, healthy volunteers (22.8 ± 1.6 SD years; 43% men) rated a range of sucrose concentrations in a taste test and underwent functional magnetic resonance imaging (fMRI) during oral delivery of water, 0.83 M, and 0.10 M sucrose. Sucrose compared to water produced robust activation in primary gustatory cortex, ventral insula, amygdala, and ventral striatum. FHP subjects displayed greater bilateral amygdala activation than FHN subjects in the low sucrose concentration (0.10 M). In secondary analyses, the right amygdala response to the 0.10 M sucrose was greatest in FHP women. When accounting for group differences in drinks per week, the family history groups remained significantly different in their right amygdala response to 0.10 M sucrose. Our findings suggest that the brain response to oral sucrose differs with a family history of alcoholism, and that this response to a mildly reinforcing primary reward might be an endophenotypic marker of alcoholism risk.