An intake structure for an internal combustion engine of a vehicle includes a cover member covering a space defined between a front side of a radiator provided in a front part of an engine room and a vehicle body opening provided in a front end of the engine room from above, and an intake duct member resting on the cover member and having an air inlet. A part of the cover member adjoining the air inlet is formed with an opening communicating the air inlet with the space, the opening defining a larger opening area in a part thereof located on a higher temperature region side of the engine room with respect to a laterally central part of the air inlet than in a part thereof located on a lower temperature region side of the engine room with respect to the laterally central part of the air inlet.