Anomalously large quantum oscillations found in the organic superconductor βH-(BEDT-TTF)2I3 are summarized. The oscillatory amplitude which is ten times larger than the residual resistance and very enhanced anharmonicity are unique among the studies performed on (BEDT-TTF)2X family. Observed results show that we have an almost perfect two-dimensional system. The abnormally enhanced third harmonic observed in certain circumstance is analysed with a relation to the splitting mechanism. We developed also a new model to explain the splitting of Shubnikov-de Haas oscillations.