In a wheel spindle device wherein a plurality of grinding wheels are attached in a juxtaposed relation to a wheel spindle rotatably carried on a wheel head of a grinding machine, a reference position for specifying a position in the circumferential direction of the grinding wheel is provided on a core member of each of the grinding wheels, and a plurality of inclined grooves at predetermined angular intervals are formed on a grinding surface of each grinding wheel to be inclined relative to the circumferential direction of each grinding wheel. In order that the fluctuations in the dynamic pressure and the grinding resistance between respective grinding wheels and workpiece portions ground therewith do not grow as a combined or synergy effect, the inclined grooves on each grinding wheel are shifted in angular phase from those on another grinding wheel, so that grinding efficiency and accuracy can be enhanced.