The angular dependent magnetoresistance oscillation (ADMRO) effect in α-(BEDT-TTF) 2-MHg(SCN) 4 [M: K, NH 4] has been studied by two-axis rotation of the crystals in magnetic field. While the ADMRO in NH 4Hg-salt is of the standard type arising from a warped cylindrical Fermi surface, that in KHg-salt is a novel type to be attributed to an open Fermi sheet. The anomalous ADMRO behavior of KHg-salt is reproduced by a model calculation based on a semiclassical trajectory of electrons on a weakly modulated open Fermi sheet.