CHISINAU, MOLDOVA - Mart 19, 2017: Captain Morgan is a brand of rum produced by alcohol conglomerate Diageo. Captain Morgan is by volume the second largest brand of spirits in the United States Shutterstock Image - CHISINAU, MOLDOVA - Mart 19, 2017: Captain Morgan is a brand of rum produced by alcohol conglomerate Diageo. Captain Morgan is by volume the second largest brand of spirits in the United States - ID: 603990887