A dimethyl ether (DME) common-rail fuel supply apparatus, may include a fuel pump fluid-connected to a fuel tank and a common rail and supplying DME fuel supplied via a fuel supply line from the fuel tank to the common rail, an injector receiving the DME fuel from the common rail and injecting the DME fuel at a predetermined pressure, a detector disposed on a fuel return line fluid-connecting the injector and the fuel tank to collect a fuel returned from the injector to the fuel tank, and a fuel amount control valve returning a portion of a fuel in the fuel pump to the fuel return line connected to the injector according to a value measured by the detector.