Animal personality can affect individual fitness and population growth. Personality traits of either parent or parents’ combination may facilitate reproduction and offspring survival across species. However, previous studies focused mainly on the role of only one sex, and the link between personality and fitness has not been confirmed in primates. We examined this link in both sexes of captive common marmosets (Callithrix jacchus), a cooperatively breeding primate with extensive paternal care. We studied the effects of five personality traits of the parents (Agreeableness, Assertiveness, Conscientiousness, Inquisitiveness, and Patience), including their absolute and directional differences within pairs, on key components of reproductive performance. We expected pairs with more similar personality scores to have higher reproductive success as found in other species with long-term pairs and biparental care, but found no evidence for this hypothesis. Instead, we detected strong effects of female traits on inter-birth intervals, which were shorter in more agreeable females, and fecundity rates, which were higher in more inquisitive females. Male traits appeared to have only a limited effect on reproductive success of the pair. Our study demonstrates that various aspects of animal personality underpin reproductive performance in captive common marmosets and provides novel insights into the possible ultimate causes of personality in cooperatively breeding species.