Extrapair fertilizations (EPFs) occur widely in socially monogamous birds and result in mixed parentage in the brood. The response of an individual to these EPFs of its social mate remains poorly investigated in terms of parental care for the mixed brood. We addressed this question in a cooperatively-breeding corvid, the azure-winged magpie Cyanopica cyana. Parentage analysis indicated that 45% of females and 37% of males engaged in EPFs. There were 49% of cooperative groups and 36% of bi-parental nests with extrapair paternity (EPP) offspring, and 22% of cooperative groups and 19% of bi-parental nests with extrapair maternity (EPM) offspring. Based on the identity of offspring, we classified adults into four types: EPP offspring fathers/mothers, EPM offspring fathers/mothers, cuckolded males/females, and faithful males/females. A comparison of provisioning rates among all four types of breeders showed that 1) EPM offspring fathers had the highest provisioning rate; 2) cuckolded males did not reduce parental care, compared to faithful males and EPP offspring fathers; and 3) females of different types did not differ in their provisioning rates. Our findings suggest that a combination of frequent opportunities, low costs of cuckoldry, and the benefits of establishing a cooperative neighbourhood can explain why EPFs occur frequently in the Tibetan population of azure-winged magpie.