There is currently a consensus about the positive effects of physical exercise on cognition. However, the exercise intensity-dependent effect on executive function remains unclear. Thus, the aim of this study was to compare the acute effects of high-intensity aerobic interval training (HIIT), progressive resistance training (PRT), or combined training (PRT + HIIT) on executive function indicators in overweight inactive adult men (aged 18–30 years old). The participants were screened and excluded for medical conditions known to impact cognitive functioning, which was measured with the Montreal Cognitive Assessment (MoCA) screening cognitive test. A randomised, parallel-group clinical trial was conducted among 36 adults who were randomly assigned to a HIIT (n = 12), PRT (n = 7), PRT + HIIT (n = 7), or control group (n = 10) until the energy expenditure of 400–500 kcal. Cognitive inhibition and attention capacity were examined using the Stroop test and d2 test of attention, respectively, and were obtained pre-exercise for baseline measurement and 1 min post-exercise for each exercise training modality. Cognitive inhibition measured by the Stroop test was improved after the HIIT protocol for the domains of reading by +5.89 (η2 = 0.33), colour naming +9.0 (η2 = 0.60), interference +10.1 (η2 = 0.39), and index interference +6.0 (η2 = 0.20). Additionally, the PRT + HIIT group had an increase for the reading condition of +7.1 (η2 = 0.40), colour naming +7.5 (η2 = 0.80), and interference +5.8 (η2 = 0.39). In regard to attentional capacity, the HIIT group elicited small to medium improvements in the concentration level domain of +21.7 (η2 = 0.44), total performance domain +56.6 (η2 = 0.50), and consistency domain −3.0 (η2 = 0.27). These results were similar in the PRT and PRT + HIIT groups in the concentration level and items-processed domains (P < 0.05). In conclusion, acute HIIT and PRT + HIIT sessions reported important effect sizes than PRT alone for cognitive inhibition and attention capacity. Taken together, the results suggest that even short-term exercise interventions can enhance overweight adults' executive functions.