High pressure X-ray diffraction study was carried out on a graphite to investigate its compressibility as well as any possible phase transition to the hexagonal diamond structure at room temperature. Energy dispersive X-ray diffraction method was introduced using a Mao-Bell type diamond anvil cell with Synchrotron Radiation. Polycrystalline sodium chloride was compressed together with graphite for the high pressure determinations. Because of the poor resolution of the X-ray diffraction pattern of graphite, its compressibility was estimated to be almost same as that of NaCl by graphite (002) X-ray diffraction peak only. An observation of any new peak from a possible hexagonal diamond phase seems very unplausible for its definite identification based on the present data. Alternative approaches such as an Wiggler Radiation source as well as a Large Volume high pressure apparatus will be necessary for the detailed studies on a graphite in future.