Socioeconomic deprivation can limit access to healthcare. Important gaps persist in the understanding of how individual indicators of socioeconomic disadvantage may affect clinical outcomes after heart transplantation. We sought to examine the impact of individual-level socioeconomic position (SEP) on prognosis of heart-transplant recipients. A population-based study including all Danish first-time heart-transplant recipients (n = 649) was conducted. Data were linked across complete national health registers. Associations were evaluated between SEP and all-cause mortality and first-time major adverse cardiovascular event (MACE) during follow-up periods. The half-time survival was 15.6 years (20-year period). In total, 330 (51%) of recipients experienced a first-time cardiovascular event and the most frequent was graft failure (42%). Both acute myocardial infarction and cardiac arrest occurred in ≤5 of recipients. Low educational level was associated with increased all-cause mortality 10–20 years post-transplant (adjusted hazard ratio [HR] 1.95, 95% confidence interval [CI] 1.19–3.19). During 1–10 years post-transplant, low educational level (adjusted HR 1.66, 95% CI 1.14–2.43) and low income (adjusted HR 1.81, 95% CI 1.02–3.22) were associated with a first-time MACE. In a country with free access to multidisciplinary team management, low levels of education and income were associated with a poorer prognosis after heart transplantation.