Recently, the personal mobility vehicle (PMV), a vehicle suitable for personal use, has been developed. It moves at low speed and is sufficiently small that it can be ridden in pedestrian space. This vehicle is expected to be a new method of transportation that is practical and environmentally friendly. As one form of PMV, the authors propose a two-wheel vehicle with two modes: a two-wheel steering and two-wheel driving bicycle mode and a parallel two-wheel mode. This vehicle has four electric motors, two for driving and two for steering, and one generator connected to the pedals. In the bicycle mode, the rider rotates the pedals to generate electric power, and the motors in the wheels produce torque using the generated energy. The front and rear wheels are steered by the electric motor according to the angle of the handle. Therefore, this bicycle is controlled by a steer-by-wire and a drive-by-wire system. In the parallel two-wheel mode, the vehicle is stabilized according to the theory of the inverted pendulum. In this paper, we focus on the bicycle mode and analyze its stability. Stabilizing the bicycle is not easy since the proposed vehicle has tires with small diameters and the traveling speed is assumed to be low. It is known that the stability of bicycles is tuned by adjusting the bicycle parameters and changing the rear steer angle. However, since we aim to use the vehicle in a narrow walking space at low speed, such conventional methods are not always suitable. The authors propose the stabilization of the bicycle using driving forces and design a controller using linear-quadratic control theory. The results of the numerical simulations show the proposed method is effective in stabilizing the bicycle.