There is disclosed a trochoid pump in which a friction between a rotor and its support portion is reduced, thereby reducing a drive torque and wear of these parts. An inner rotor of the trochoid-type fuel pump is rotatably supported by a bushing through a bearing. An outer rotor is rotatably received in an inner periphery of a spacer. A first groove is formed in a portion of the outer periphery of the bushing disposed close to a discharge port, and a discharge fuel is introduced into this groove. A second groove is formed in a portion of the inner periphery of the spacer disposed close to the discharge port, and the discharge fuel is introduced into this groove. Although the inner rotor is urged toward the bushing by the fuel pressure of the discharge port, the urging force to urge the inner rotor toward the bushing is weakened by the discharge fuel introduced into the first groove, thereby reducing a friction. Although the outer rotor is urged against the spacer, the urging force to urge the outer rotor against the spacer is weakened by the discharge fuel introduced into the second groove, thereby reducing a friction.