Provided is a cooling control device of an internal-combustion engine with which it is possible, by restricting a cooling water pressure differential between an engine cooling circuit and an intercooler cooling circuit, to cause the cooling water to flow appropriately from one of the two cooling circuits to the other cooling circuit, even if a valve between the two cooling circuits is open to a large degree. In a connecting passage between an engine cooling circuit 50 and an intercooler cooling circuit 60, a cooling water inflow passage 71 is connected between a location that is downstream of a mechanical pump 53 and upstream of a main radiator 51, in the engine cooling circuit 50, and a location that is downstream of a sub-radiator 61 and upstream of an electric pump 63, in the intercooler cooling circuit 60. A cooling water outflow passage 72 is connected between a location that is downstream of the electric pump 63 and upstream of the sub-radiator 61, in the intercooler cooling circuit 60, and a location that is downstream of the mechanical pump 53 and upstream of the main radiator 51, in the engine cooling circuit 50, and an inter-cooling-circuit valve 73 is provided in the cooling water inflow passage 71.