Bicycle is one of convenient transportation system. In this paper, we derive a more precise kinematics of bicycle system compared with other ones which were suggested by other researchers. In the derivation of kinematics we adopted a physical concept called virtual wheel. We also propose an algorithm for deriving inverse kinematics of a bicycle system. In this paper, the meaning of inverse kinematics is to find the time functions of steering angle and driving wheel speed for a given desired path trajectory. From the computer simulation, we show the validity of our proposed algorithm for inverse kinematics of bicycle system.