Now the lithium ion batteries are widely used in electrical vehicles (EV). The battery modeling and state estimation is of great significance. The rigorous physic based electrochemical model is too complicated for on-line simulation in vehicle. In this work, the simplification of physics-based model lithium ion battery for application in battery management system (BMS) on real electrical vehicle is proposed. Approximate method for solving the solid phase diffusion and electrolyte concentration distribution problems is introduced. The approximate result is very close to the rigorous model but fewer computations are needed. An extended single particle model is founded based on these approximated results and the on-line state of charge (SOC) estimation algorithm using the extended Kalman filter with this single particle model is discussed. This SOC estimation algorithm could be used in the BMS in real vehicle.