To keep a good cooling performance conformed to each system up to a range from a medium and low speed area to the high speed one and to maintain output characteristics, in the cooling system which utilizes cooling water, taken out of a water jet propulsion pump, for the cooling of an engine and an exhaust system.

Cooling water to be taken out of a positive pressure part 3a of a water jet propulsion pump 2 is divided into two parts, a first cooling water route 41 to supply it to a cylinder and a cylinder head 7 and a second cooling water route 42 to supply it to an exhaust pipe unit including an exhaust expansion chamber 11 separately from the route. Dimension of exhaust expansion chamber 11 is set to be synchronized to an exhaust pressure wave in time of a medium and low speed area, for example, while in time of a high speed area, a cooling water quantity is held low by a control unit, whereby it is synchronized to the exhaust pressure wave.