A cooling system of an internal combustion engine of a motorcycle, which has a suction side guard (4), enables a high ratio between the open surface of the guard and its overall surface, ensuring an improved penetration of the air through the radiator and thus avoiding oversizing of the suction fan, wherein: said guard (4), having a lower edge (6), an upper edge (7), a front edge (8) and a rear edge (9) with respect to a running direction (F) of the vehicle, has a grate mesh structure extending on a plane whereby a deviation space (12) of motion of the air sucked by the fan is defined behind the guard (4); said grate mesh structure being surrounded by a rib (13) having, at the front edge (8), a lower height than that at the rear edge (9).