Odontocetes are usually reported giving birth to calves in breech position (fluke-first). Cephalic position (head-first) is less frequently observed and, therefore, is considered to be abnormal for the parturition. However, the influence of the calf position at birth on the parturition process and calf survival has not been thoroughly studied. More information is needed to improve the captive breeding success of odontocetes—especially for endangered species such as finless porpoises (Neophocaena asiaeorientalis). In this study, we observed the labor of eight captive finless porpoises (N. asiaeorientalis asiaeorientalis and N. a. sunameri). The duration of parturition and the time of particular events in the parturition process were recorded for both breech and cephalic births. Cephalic births were shorter than breech births, and the calf position at birth did not seem to have a negative effect on its survival. The results presented herein could be used as recommendations to improve the management of future parturitions of captive finless porpoises by ensuring the safety of both cows and calves, potentially increasing the survival rate of calves. Better management of the parturition process could facilitate the improvement of the captive breeding success of these endangered species.