The specimens of two new records of lamniform shark (Chondrichthyes: Lamniformes) were collected in the waters off eastern Taiwan. They are Megachasma pelagios Taylor, Compagno & Struhsaker, 1983 (Megachasmidae) and Mitsukurina owstoni Jordan, 1898 (Mitsukurinidae). The monotypic families Megachasmidae and Mitsukurinidae which both have only one species in each family are new records to Taiwan. Megamouth shark, Megachasma pelagios, were collected by trawlers off Hualien County and Taitung County, and goblin shark, Mitsukurina owstoni, were collected by bottom trawlers in the waters off Tashi and Nanfangao harbors. This paper includes diagnostic characters and geographical distributions of the two species. Color photos and a key to the families of the order Lamniformes from Taiwan are given.