This shoulder prosthesis glenoid component (2) has on one of its faces an articulation surface (SA) adapted to cooperate with a humeral head and having, on an opposite face (SG) adapted to be immobilized on the glenoid cavity (G) of a shoulder, a keel (4) for anchoring it in the glenoid cavity (G). This keel (4) comprises a body (5) that extends from the opposite face (SG). The keel (4) comprises at least one fin (6) projecting from the body (5) which runs over at least a part of the perimeter of the body (5).