The invention provides a plane, inner arc and outer arc grinding machine and a grinding method thereof, which relate to the technical field of machining and solve the technical problem that a plane, an inner arc and an outer arc cannot be finished on the same grinding machine. The plane, inner arc and outer arc grinding machine comprises a base, a swing arm support, a swing arm, work fixtures, and a grinding mechanism, a working platform is arranged on the base; the swing arm is articulated with the swing arm support, and can swing within a horizontal plane; the work fixtures are detachably arranged on the head of the swing arm, and the work fixtures include an inner arc-grinding fixture, an outer arc-grinding fixture, and a plane-grinding fixture. Since the inner arc-grinding fixture, the outer arc-grinding fixture and the plane-grinding fixture are detachably arranged on the head of the swing arm, an inner arc, an outer arc and a plane can be ground on the same grinding machine, moreover, choice is flexible according to the requirements of production, not only are investments and production costs of manufacturing enterprises reduced, but also the service efficiency of the equipment is increased, and enterprise incomes are increased.