Human immunodeficiency virus (HIV)-associated neurocognitive disorders can persist in many patients despite achieving viral suppression while on antiretroviral therapy (ART). Neurocognitive function over 48 weeks was evaluated using a Cogstate test battery assessing psychomotor function, attention, learning, and working memory in 293 HIV-1-infected, ART-experienced, and virologically suppressed adults. The ASSURE study randomized participants 1:2 to remain on tenofovir/emtricitabine (TDF/FTC) and ritonavir-boosted atazanavir (ATV/r) or simplify to abacavir/lamivudine + atazanavir (ABC/3TC + ATV). Neurocognitive z-scores were computed using demographically adjusted normative data and were classified as “impaired” (defined as either a z-score ≤ - 2 or having 2 or more standardized individual test z-scores ≤ - 1); while higher scores (equaling better performance) were classified as “normal”. By z-scores, 54.7% of participants had impaired neurocognition at baseline and 50.2% at week 48. There were no significant differences (p < 0.05) in the baseline-adjusted performance between treatment groups for any individual test or by z-score. Specific demographic and medical risk factors were evaluated by univariate analysis for impact on neurocognitive performance. Factors with p < 0.10 were evaluated by backwards regression analysis to identify neurocognition-correlated factors after accounting for treatment, assessment, and baseline. Four risk factors at baseline for impaired neurocognition were initially identified: lower CD4 nadir lymphocyte counts, higher Framingham risk scores, and interleukin-6 levels, and a history of psychiatric disorder not otherwise specified, however none were found to moderate the effect of treatment on neurocognition. In this aviremic, treatment-experienced population, baseline-adjusted neurocognitive function remained stable and equivalent over 48 weeks with both TDF/FTC + ATV/r-treated and in the ART-simplified ABC/3TC + ATV treatment groups.