The COVID-19 virus has a neuropsychiatric impact, including mild cognitive impairment. Most severe traumas negatively impact executive functions. However, the impact of COVID-19 trauma on cognition is unknown. To test the effects of COVID-19 traumatic stress on executive functions, we surveyed 417 Syrian refugees using measures for COVID-19 traumatic stress, executive functions, PTSD, depression, and anxiety. Using step multiple regression and PROCESS mediation analysis, COVID-19 traumatic stress and its three fears, economic and social components, directly and indirectly, affect increased working memory and inhibition deficits via PTSD and depression. We discussed the conceptual and clinical implications of the results.