A sealing system for a gap (2) existing between the fuselage (3) and the elevator (4) of a orientable horizontal stabilizer (5) of an aircraft, comprises a main body (1) formed by an upper surface (18) and a lower surface (19) and at least one longitudinal vertical element (22) arranged between the two surfaces (18,19) which grants rigidity to the main body (1), and a plurality of first elastic sealing profiles (9) between the first surface (11) of the main body (1) and the outer surface of the fuselage (3) and making contact with them, and a plurality of second elastic sealing profiles (13) between the second surface (12) of the main body (1) and the first end of the elevator (15) and making contact with them, in such a way that the sealing of the gap (2) takes place and an aerodynamic continuity is produced between the fuselage (3) and the elevator (4) when the elevator (4) is at rest in the plane of the orientable horizontal stabilizer (5) for any of the orientation positions of the orientable horizontal stabilizer (5).