A saddle-riding vehicle comprising: a vehicle frame structure; a drive source supported by the vehicle frame structure; and a radiator for radiating heat from a cooling medium in the drive source wherein the radiator is fitted to the vehicle frame structure, and the radiator comprises: a core through which the cooling medium flows; a cooling fan disposed on a downstream side of the core with respect to a flow direction of an incoming wind and configured to ventilate the core; a fan covering opened downwardly and configured to enclose regions above the cooling fan, opposite sides of the cooling fan and a downstream side of the cooling fan with respect to the flow direction, wherein a partition wall partitioning between a lower portion of the core and a lower portion of the cooling fan is provided radially outwardly of a front portion of the cooling fan, wherein the partition wall is operable to suppress a backflow of discharge air through an opening from flowing into the core, wherein the axial position of a front surface of the partition wall is in flush with a front surface of a rotary vane assembly of the cooling fan, wherein the core is supported by a frame assembly, which is rectangular in shape when viewed from front and which encloses the periphery of a plurality of fins, characterized in that the partition wall protrudes downwardly from an undersurface of the frame assembly, wherein the fan covering is fitted to the frame assembly of the core by means of screws through a plurality of mounting pieces provided in an outer periphery of the fan covering, and the fan covering, the partition wall and the mounting pieces are formed as a one piece structure and the fan covering, when viewed in a direction along a shaft axis of the cooling fan, is of a generally inverted U-shape having a reduced width in an upper portion thereof and a large width in a lower portion thereof. a vehicle frame structure; a drive source supported by the vehicle frame structure; and a radiator for radiating heat from a cooling medium in the drive source wherein the radiator is fitted to the vehicle frame structure, and the radiator comprises: a core through which the cooling medium flows; a cooling fan disposed on a downstream side of the core with respect to a flow direction of an incoming wind and configured to ventilate the core; a core through which the cooling medium flows; a cooling fan disposed on a downstream side of the core with respect to a flow direction of an incoming wind and configured to ventilate the core; a fan covering opened downwardly and configured to enclose regions above the cooling fan, opposite sides of the cooling fan and a downstream side of the cooling fan with respect to the flow direction, wherein a partition wall partitioning between a lower portion of the core and a lower portion of the cooling fan is provided radially outwardly of a front portion of the cooling fan, wherein the partition wall is operable to suppress a backflow of discharge air through an opening from flowing into the core, wherein the axial position of a front surface of the partition wall is in flush with a front surface of a rotary vane assembly of the cooling fan, wherein the core is supported by a frame assembly, which is rectangular in shape when viewed from front and which encloses the periphery of a plurality of fins, characterized in that the partition wall protrudes downwardly from an undersurface of the frame assembly, wherein the fan covering is fitted to the frame assembly of the core by means of screws through a plurality of mounting pieces provided in an outer periphery of the fan covering, and the fan covering, the partition wall and the mounting pieces are formed as a one piece structure and the fan covering, when viewed in a direction along a shaft axis of the cooling fan, is of a generally inverted U-shape having a reduced width in an upper portion thereof and a large width in a lower portion thereof.