Seabirds are long-lived birds that invest in offspring at very high levels, for which male parental care is indispensable. These characteristics are thought to explain seabirds’ generally low level of extra-pair paternity (EPP). Although the Streaked Shearwater (Calonectris leucomelas) is a socially monogamous seabird, it is known to copulate outside its social pair bond, which implies the frequent occurrence of EPP. In the closely related Cory’s Shearwater Calonectris borealis, cuckoldry is related to body size of the social male. To determine whether body-size-related EPP occurs among Streaked Shearwaters, we established 39 new microsatellite markers for parentage analysis and compared body size between cuckolded and non-cuckolded males. With the new markers, we found that extra-pair males sired 17 (15.0%) of 113 offspring during the 2014–2016 study period, which included three 1.5-month chick-rearing periods. This percentage is among the highest recorded for seabirds. We also found the bill and wing length of cuckolded males to be significantly shorter than those of non-cuckolded males, and that females can reject attempted copulations. These observations imply that EPP in this species is size related and involves female acceptance.