Depression in adolescence is common worldwide, with the burden being highest in low- and middle-income countries. This study assessed the efficacy of in-person Memory Specificity Training (MeST) and computerized MeST (c-MeST) as cognitive training programs aimed at addressing depression among Iranian adolescents. A secondary aim was to evaluate the efficacy of MeST and c-MeST on autobiographical memory specificity, emotion regulation and cognitive control. Ninety Iranian male adolescents (aged 13–18 years) with depression were randomly assigned to three groups; MeST group (n = 30), c-MeST group (n = 30) and the non-active control group (n = 30). Participants completed the Beck Depression Inventory-II, Autobiographical Memory Test, Cognitive Emotion Regulation Questionnaire, Wisconsin Card Sorting Test and Stroop Color and Word Test. The groups underwent either MeST and c-MeST. All the assessments were re-conducted after the intervention (post-intervention) and at 1-month post-intervention (follow-up). The in-person MeST group exhibited significantly higher autobiographical memory specificity at post-intervention and follow-up compared to the c-MeST group. Both groups demonstrated significantly lower levels of depression at post-intervention and follow-up. Both groups showed improvements in emotion regulation and cognitive control, which were found to mediate improvements in depression symptomatology. c-MeST and MeST appear promising brief interventions for the treatment of depression among adolescents in Iran.