Background There is growing concern about the health impact of heavy alcohol use in people infected with human immunodeficiency virus (HIV+). Mixed findings of past studies regarding the cognitive impact of alcohol use in HIV+ adults have been mixed, with inconsistent evidence that alcohol consumption exacerbates HIV‐associated brain dysfunction. This study examined contributions of current heavy drinking, lifetime alcohol use disorder (AUD), and age to cognitive deficits in HIV+ adults, and relative to other HIV‐associated clinical factors. Methods Cognitive performance of HIV+ adults (n = 104) was assessed, and comparisons were made between heavy current to nonheavy drinkers (NIAAA criteria), lifetime AUD versus no‐AUD, and older (>50 years) versus younger participants. Hierarchical regression analyses were conducted to examine the association between cognitive performance and current heavy drinking, lifetime AUD, and older age, while also correcting for HIV clinical factors and history of other substance use. Results Individuals reporting current heavy drinking and meeting criteria for lifetime AUD demonstrated the greatest degree of deficits across multiple cognitive domains. Deficits were greatest among HIV+ adults with lifetime AUD, and older age was also associated with weaker cognitive performance. Lifetime AUD and older age independently exhibited stronger associations with cognitive performance than HIV clinical factors (e.g., viral load, current CD4, and nadir CD4) or past opiate and cocaine use. Conclusions Current heavy drinking and lifetime AUD adversely affect cognitive function in HIV+ adults. Greatest deficits existed when there was a history of AUD and continued current heavy drinking, indicating that past AUD continues to have an adverse impact and should not be ignored. That alcohol use was more strongly associated with cognitive performance than HIV clinical factors underscore clinical importance of targeting reduction in heavy alcohol consumption in HIV+ adults.