This paper proposes a novel dynamic stable grasping method of an arbitrary polyhedral object for a hand-arm system with hemispherical fingertips. This method makes it possible to satisfy the force/torque equilibrium condition for the immobilization of the object without knowledge of the object. Two control signals are proposed which generate grasping forces normal and tangential to an object surface in a final state. The dynamics of the overall system is modeled and analyzed theoretically. We demonstrate the stable grasping of an arbitrary polyhedral object using the proposed controller through numerical simulations and experiments using a newly developed mechanical hand-arm system.