A two-wheeled motor vehicle, comprising: a vehicle body frame; a storage box supported by the vehicle body frame; a seat placed above the storage box, being capable of opening and closing an opening defined by an upper edge of the storage box; the upper edge of the storage box comprising the upper edges of two spaced lateral walls of the storage box; and a cover placed beside the storage box, wherein a lateral part of a bottom surface of the seat is bent downward, and opposed to a lateral surface of a first of the two spaced lateral walls of the storage box so as to go farther away from the lateral surface of said first lateral wall of the storage box as it goes downward, an upper edge of the cover is positioned, in a side view, higher than a lower edge of a lateral part of the seat and lower than the upper edge of said first lateral wall of the storage box, a clearance is formed between the lateral surface of said first lateral wall of the storage box and the upper edge of the cover, no flange that spreads outward is formed on the upper edge of said lateral wall of the storage box the lateral surface of said first lateral wall of the storage box has a projection formed thereon at a position lower than the upper edge of said first lateral wall of the storage box, the projection overlapping the upper edge of the cover in a plan view, in which a part of the lateral surface above the projection is formed as a flat surface up to the upper edge of the lateral wall of the storage box, and the projection extends above and along the upper edge of the cover, the two-wheeled motor vehicle being characterized in that: the two spaced lateral walls of the storage box form a storage space which continues to a space between the lateral part of the bottom surface of the seat and the lateral surface of said first lateral wall of the storage box through a clearance between the bottom surface of the seat and the upper edge of the lateral wall of the storage box when the seat is positioned leaving the opening of the storage box close. a vehicle body frame; a storage box supported by the vehicle body frame; a seat placed above the storage box, being capable of opening and closing an opening defined by an upper edge of the storage box; the upper edge of the storage box comprising the upper edges of two spaced lateral walls of the storage box; and a cover placed beside the storage box, wherein a lateral part of a bottom surface of the seat is bent downward, and opposed to a lateral surface of a first of the two spaced lateral walls of the storage box so as to go farther away from the lateral surface of said first lateral wall of the storage box as it goes downward, an upper edge of the cover is positioned, in a side view, higher than a lower edge of a lateral part of the seat and lower than the upper edge of said first lateral wall of the storage box, a clearance is formed between the lateral surface of said first lateral wall of the storage box and the upper edge of the cover, no flange that spreads outward is formed on the upper edge of said lateral wall of the storage box the lateral surface of said first lateral wall of the storage box has a projection formed thereon at a position lower than the upper edge of said first lateral wall of the storage box, the projection overlapping the upper edge of the cover in a plan view, in which a part of the lateral surface above the projection is formed as a flat surface up to the upper edge of the lateral wall of the storage box, and the projection extends above and along the upper edge of the cover, the two-wheeled motor vehicle being characterized in that: the two spaced lateral walls of the storage box form a storage space which continues to a space between the lateral part of the bottom surface of the seat and the lateral surface of said first lateral wall of the storage box through a clearance between the bottom surface of the seat and the upper edge of the lateral wall of the storage box when the seat is positioned leaving the opening of the storage box close.