People living with HIV can experience posttraumatic stress disorder (PTSD). Complex relationships exist between HIV, PTSD and cognitive impairments. This cross-sectional study compared three cognitive impairments (false memory, attentional bias, deficits in future thinking) among people living with HIV with and without PTSD in Iran. People living with HIV with PTSD (n = 20) and without PTSD (n = 20) completed measures of psychological symptomatology, dot-probe task, Deese Roediger McDermott paradigm and future thinking task at Razavi Khorasan Health Center. The PTSD group, when compared to the non-PTSD group, recognised a significantly greater number of false memories (p < 0.001; [eta] [superscript 2] = 0.58), had an attentional bias toward threat-related words (p < 0.001; [eta] [superscript 2] = 0.35) and imagined fewer specific future events (p < 0.001; [eta] [superscript 2] = 0.31). People living with HIV with PTSD may have difficulties with false memory, attentional biases, and generating future events. Since psychological treatments are limited in Iran, this research highlighted some potential cognitive targets for people living with HIV.