Some older adults with human immunodeficiency virus (HIV) experience poor sleep which can worsen cognition. Transcranial direct current stimulation (tDCS) and cognitive training have improved sleep and cognition in studies of older adults; yet, their combined influence is unknown in adults with HIV. Older adults with HIV (n = 33) and without HIV (n = 33) were randomized to receive 10 one-hour sessions of speed of processing (SOP) training with tDCS or sham tDCS over approximately 5 weeks. tDCS with SOP training did not improve sleep. Omitting correction of multiple comparisons for this exploratory pilot study, main effects for HIV (F[1, 59] = 5.26, p = .03, ηp2 = .082) and tDCS (F[1, 59] = 5.16, p = .03, ηp2 = .080) on the Digit Copy Test were detected. A HIV × tDCS interaction was detected on the Letter Comparison Test (F[1, 59] = 5.50, p = .02, ηp2 = .085). Useful Field of View scores improved across all four groups (F[1, 59] = 64.76, p < .001, ηp2 = .523). No significant effects for HIV (F[1, 59] = 1.82, p = .18) and tDCS (F[1, 59] = .01, p = .94) were detected on the Useful Field of View test. While the current study did not show effects of combined tDCS and SOP training on sleep quality, future studies are needed to examine the effects of such interventions on sleep-related cognitive functions among cognitively impaired adults with HIV.