A positive-displacement oil pump is disclosed. In the oil pump, an insert body is fitted into a central opening of a shaft body to a height of an oil-feeding hole. The insert body is rotated along with the shaft body, and includes a central hole formed in the insert body, a cylindrical lip formed around an outlet of the central hole, a fluid discharge diode provided in an inlet of the central hole, and an inclined groove formed around an outer circumferential surface of the insert body such that the inclined groove forms a closed curve. A piston is movably fitted over the insert body such that the piston is axially moved while changing a volume of a displacement space defined between the insert body and the piston.