Half of people with HIV (PWH) have HIV-associated neurocognitive disorder (HAND). This study examined whether cognition can be improved using a framework targeting impaired individual cognitive domains in PWH with HAND. In this two-group pre-post experimental design study, 88 adults with HAND were randomized to either: (1) a no-contact control group (n = 40) or (2) the Individualized-Targeted Cognitive Training group (n = 48). Baseline cognitive performance was assessed on eight cognitive domains. A theoretical framework was used to determine the two cognitive domains selected for training. With priority on speed of processing (SOP) and attention impairments, participants received SOP and/or attention training if such impairments were detected; if not, participants were assigned to cognitive training in one/two of the least impaired cognitive domains contributing to their HAND diagnosis. Global cognitive score was slightly improved following training (p = 0.256; d = − 0.21), but it was not significant. Significant improvements were observed on SOP following training in that domain (SOP; d = − 0.88; p = 0.011). SOP training also improved functioning in other cognitive domains. This individualized cognitive intervention did not change HAND status, but it did result in improved SOP, in turn yielding improvement in other cognitive domains.