The aim of the present study was to investigate the association between grandiose narcissism and the feeling of distress. We referred to the narcissistic admiration and rivalry model. We hypothesized that people with high narcissistic admiration would experience less distress and fear and that intellectual self-confidence would account for this relationship. We examined two dimensions of grandiose narcissism using Narcissistic Admiration and Rivalry Questionnaire, self-assessed intelligence, and various aspects of distress in two studies. In Study 1 (N = 170), we assessed distress (with the Dundee Stress State Questionnaire), related to performance in an intelligence test (Raven’s Advanced Progressive Matrices), and in Study 2 (N = 258) we measured fear related to the COVID-19 pandemic. In both studies, narcissistic admiration was inversely related to distress/fear, and this relationship was fully mediated by self-assessed intelligence. Narcissistic rivalry was unrelated to both distress and self-assessed intelligence. These findings emphasize the importance of self-views related to intelligence for those with high narcissistic admiration. In particular, intellectual self- confidence plays an important role in reducing distress among narcissists.