BACKGROUND: The associations of cause-specific mortality with alcohol consumption have been studied mainly in higher-income countries. We relate alcohol consumption to mortality in Cuba. METHODS: In 1996-2002, 146 556 adults were recruited into a prospective study from the general population in five areas of Cuba. Participants were interviewed, measured and followed up by electronic linkage to national death registries until January 1, 2017. After excluding all with missing data or chronic disease at recruitment, Cox regression (adjusted for age, sex, province, education, and smoking) was used to relate mortality rate ratios (RRs) at ages 35-79 years to alcohol consumption. RRs were corrected for long-term variability in alcohol consumption using repeat measures among 20 593 participants resurveyed in 2006-08. FINDINGS: After exclusions, there were 120 623 participants aged 35-79 years (mean age 52 [SD 12]; 67 694 [56%] women). At recruitment, 22 670 (43%) men and 9490 (14%) women were current alcohol drinkers, with 15 433 (29%) men and 3054 (5%) women drinking at least weekly; most alcohol consumption was from rum. All-cause mortality was positively and continuously associated with weekly alcohol consumption: each additional 35cl bottle of rum per week (110g of pure alcohol) was associated with ∼10% higher risk of all-cause mortality (RR 1.08 [95%CI 1.05-1.11]). The major causes of excess mortality in weekly drinkers were cancer, vascular disease, and external causes. Non-drinkers had ∼10% higher risk (RR 1.11 [1.09-1.14]) of all-cause mortality than those in the lowest category of weekly alcohol consumption (<1 bottle/week), but this association was almost completely attenuated on exclusion of early follow-up. INTERPRETATION: In this large prospective study in Cuba, weekly alcohol consumption was continuously related to premature mortality. Reverse causality is likely to account for much of the apparent excess risk among non-drinkers. The findings support limits to alcohol consumption that are lower than present recommendations in Cuba. FUNDING: Medical Research Council, British Heart Foundation, Cancer Research UK, CDC Foundation (with support from Amgen).