A water pump for cooling an engine in which an impeller accommodated in a pump housing provided on an engine body is mounted on an end of a rotational shaft rotatably supported on the pump housing for enhancing the reliability of the mounting strength of the impeller while avoiding an increase in cost. A fitting recess for fitting an end of the rotational shaft having an outer circumferential surface which is straight in an axial direction at least in a portion on the impeller side is provided in a central portion of the impeller. A bolt inserted into the central portion of the impeller is threaded in a coaxial direction with the end of the rotational shaft in a state that is fitted in the fitting recess.