This paper presents a new type of holonomic and omnidirectional mobile robot. A steered driving wheel for holonomic and omnidirectional robots is proposed which has an offset distance between the steering axle and the wheel axle along a direction of wheel traveling like a caster which can use a conventional tires (a rubber tire or a pneumatic tire) . A kinematics of the wheel mechanism is analyzed and a new control strategy is introduced to avoid a nonholonomic constraints on the wheels. The driving wheel realizes an active ”caster motion”which enables 2DOF motions in the two dimensional plane. The concept of a holonomic robot with the proposed driving wheels is implemented and tested on a two-wheeled vehicle prototype. Experimental results show that the prototype robot realizes smooth holonomic and omnidirectional motions and precise mobility.