A cooling structure for an internal combustion engine comprising: an engine main unit including a crankcase portion, a cylinder portion, and a cylinder head portion, the cylinder portion and the cylinder head portion having therein a cylinder coolant jacket and a cylinder head coolant jacket, respectively; a coolant pump for circulating coolant through a coolant circulation path formed in the cylinder coolant jacket and the cylinder head coolant jacket, the coolant circulation path including a radiator-routing passage (Pr) by way of a radiator and a bypass passage (Pb) bypassing the radiator; and a thermostat valve for changing over between coolant circulation through the radiator-routing passage (Pr) and coolant circulation through the bypass passage (Pb); wherein: the thermostat valve includes a first valve for opening and closing the radiator-routing passage (Pr), and a second valve for opening and closing the bypass passage (Pb), the first valve and the second valve being operable concurrently; the cylinder coolant jacket is disposed around a cylinder bore in the cylinder portion and is partitioned into two in a cylinder axis direction to thereby form a main cylinder coolant jacket on a side of the cylinder head portion and a sub-cylinder coolant jacket on a side of the crankcase portion; and the bypass passage (Pb) is formed partly by the sub-cylinder coolant jacket. an engine main unit including a crankcase portion, a cylinder portion, and a cylinder head portion, the cylinder portion and the cylinder head portion having therein a cylinder coolant jacket and a cylinder head coolant jacket, respectively; a coolant pump for circulating coolant through a coolant circulation path formed in the cylinder coolant jacket and the cylinder head coolant jacket, the coolant circulation path including a radiator-routing passage (Pr) by way of a radiator and a bypass passage (Pb) bypassing the radiator; and a thermostat valve for changing over between coolant circulation through the radiator-routing passage (Pr) and coolant circulation through the bypass passage (Pb); wherein: the thermostat valve includes a first valve for opening and closing the radiator-routing passage (Pr), and a second valve for opening and closing the bypass passage (Pb), the first valve and the second valve being operable concurrently; the cylinder coolant jacket is disposed around a cylinder bore in the cylinder portion and is partitioned into two in a cylinder axis direction to thereby form a main cylinder coolant jacket on a side of the cylinder head portion and a sub-cylinder coolant jacket on a side of the crankcase portion; and the bypass passage (Pb) is formed partly by the sub-cylinder coolant jacket. the thermostat valve includes a first valve for opening and closing the radiator-routing passage (Pr), and a second valve for opening and closing the bypass passage (Pb), the first valve and the second valve being operable concurrently; the cylinder coolant jacket is disposed around a cylinder bore in the cylinder portion and is partitioned into two in a cylinder axis direction to thereby form a main cylinder coolant jacket on a side of the cylinder head portion and a sub-cylinder coolant jacket on a side of the crankcase portion; and the bypass passage (Pb) is formed partly by the sub-cylinder coolant jacket.