An oil supply apparatus for an engine provided with a two-stage relief valve, comprising: an oil pump housing having an inlet side and an outlet side configured to enable entry and exit of a working fluid; - a rotor mounted in the oil pump housing and driven in proportion to an engine speed; a relief valve operated by a pressure of the working fluid between the inlet side and the outlet side; and first and second flow paths (400, 500) formed between the inlet side and the relief valve, wherein the relief valve is elastically supported and opened in a sequence from a low speed, a medium speed, a medium/high speed, and a high speed in proportion to the engine speed, and a working fluid amount of the outlet side is returned to the inlet side through the first or second flow path (400 or 500) in proportion to the engine speed at the medium speed and the high speed, SAID APPARATUS BEING CHARACTERISED IN THAT the relief valve blocks the first and second flow paths (400, 500) regardless of the working fluid pressure of the outlet side when the rotor is rotated at the low speed, is opened by a hydraulic pressure of the outlet side to return a portion of the working fluid of the outlet side to the inlet side through the second flow path when the rotor is rotated at the medium speed, is further opened by the hydraulic pressure of the outlet side to block the first and second flow paths (400, 500) when the rotor is rotated at the medium/high speed, and is opened by the hydraulic pressure of the outlet side to return a portion of the working fluid of the outlet side to the inlet side through the first flow path when the rotor is rotated at the high speed. an oil pump housing having an inlet side and an outlet side configured to enable entry and exit of a working fluid; - a rotor mounted in the oil pump housing and driven in proportion to an engine speed; - a rotor mounted in the oil pump housing and driven in proportion to an engine speed; a relief valve operated by a pressure of the working fluid between the inlet side and the outlet side; and first and second flow paths (400, 500) formed between the inlet side and the relief valve, wherein the relief valve is elastically supported and opened in a sequence from a low speed, a medium speed, a medium/high speed, and a high speed in proportion to the engine speed, and a working fluid amount of the outlet side is returned to the inlet side through the first or second flow path (400 or 500) in proportion to the engine speed at the medium speed and the high speed, SAID APPARATUS BEING CHARACTERISED IN THAT the relief valve blocks the first and second flow paths (400, 500) regardless of the working fluid pressure of the outlet side when the rotor is rotated at the low speed, is opened by a hydraulic pressure of the outlet side to return a portion of the working fluid of the outlet side to the inlet side through the second flow path when the rotor is rotated at the medium speed, is further opened by the hydraulic pressure of the outlet side to block the first and second flow paths (400, 500) when the rotor is rotated at the medium/high speed, and is opened by the hydraulic pressure of the outlet side to return a portion of the working fluid of the outlet side to the inlet side through the first flow path when the rotor is rotated at the high speed.