Provided is a cooling structure of an internal-combustion engine capable of achieving both a quick warm-up and effective cooling of a cylinder block while suppressing upsizing of the cylinder block or an increase in pressure loss of cooling water. With respect to a block-side water jacket (7A) formed in a ring shape so as to surround a cylinder (2), a movable partition member (31) that can be put in a closed position at which the block-side water jacket (7A) is partitioned in a circumference direction and an open position at which the block-side water jacket (7A) is opened in the circumference direction is provided between a cooling-water entrance (21) and a main-cooling-water exit (22m). In an open state (7A) in which the movable partition member (31) is put in the open position, cooling water directly flows into the main-cooling-water exit (22m) to attain a quick warm-up. On the other hand, in the closed state (7B) in which the movable partition member (31) is put in the closed position, the cooling water f
