Cognition plays a major role in an animal’s interactions with its environment, but despite its impacts on fitness, the action of sexual selection on cognition remains poorly understood. In monogamous species with bi-parental care, females obtain direct benefits through male parental care. Male cognition can directly impact offspring quality by mediating the ability to obtain resources. Thus, it is expected that females select mates with high cognitive performance. We tested the hypothesis that females prefer males with higher cognitive abilities in a small parrot, the budgerigar (Melopsittacus undulatus). 30 males were tested on 4 cognitive tasks: problem solving, spatial memory, seed discrimination, and detour reaching. We also measured personality traits, aggressiveness, sociability, and male body condition. Male pairing success was determined with a free-pairing experiment with 5 mixed-sex groups, each composed of 6 males and 3 females. Males varied substantially in performance in all cognitive tasks. Male composite cognitive score, an integrative measure of male cognitive performance, showed a bimodal distribution. However, we did not find a significant effect of male cognitive abilities on male pairing success. We further tested the effect of personality, aggressiveness, sociability, and body condition on female mate choice. None of these variables had significant effects on mate choice. Females may rely on other indicators of male quality rather than male cognitive abilities when selecting a mate. It is possible that male cognitive skills play a role in other aspects of female mating decisions, such as extra-pair copulations or in decisions concerning investment in reproduction.