The pelagic thresher shark (Alopias pelagicus) is the dominant bycatch that landed at the Kutaraja Ocean Fishing Port. This species has been considered endangered and listed under CITES Appendix II. Some fishers of purse seiners and handliners from Kutaraja Fishing Port catch the thresher sharks, but the catch is considered the bycatch of these types of fishing fleets. These fishing practices have promoted conflict among fishers and illegal fishing practices and reduced the income of the fishers. This study aims to assess the management status of A. pelagicus fishery involving the purse seiners and handliners by EAFM framework; and to formulate management measures promoting the sustainability of the shark population based on social, economic, and institutional aspects. This research was conducted through field measurement and interviews with key stakeholders. A composite index technique analyzed data in frame of EAFM. The social aspect of the fisheries management showed a ‘very good’ status (score of 83.3%), while the economic aspect was of ‘good’ category (score of 66.7%) and the institutional governance aspect was of ‘poor’ category (score of 33.3%). Thus, the institutional aspect of management needs to be improved to achieve sustainability of the pelagic thresher shark fishery in terms of socio-economic and governance. This study recommends the implementation of a profit-sharing system as regulated by the government, implementing local wisdom related to fisheries, reducing sharks for local consumption and trading, formulating sustainable shark policy, providing facilities and conducting regular monitoring action for shark fisheries.