An oil pump includes a pump cover covering a recess in a side face of a pump body to form a gear compartment therebetween. A drive gear and a rotatably driven gear are meshed and mounted in the gear compartment. Working spaces R are formed by the engagement of the meshed gear teeth. Discharge ports are formed in both the pump body and the pump cover in communication with the gear compartment. A notch is formed in the pump body at the bottom of the gear compartment and extends from the front end of the discharge port in the pump body to the rear end of a discharge area for the working spaces. Another notch is formed in the inner side face of the pump cover, and extends from the front end of the discharge port in the cover to the rear end of the discharge area.