A new approximate physics-based Lithium-ion cell model is developed by extending the descriptions of the non-uniform reaction distribution effect and the electrolyte concentration/potential distribution effect into single particle model, namely the extended single particle model. In this model, the simplification of the solid-phase diffusion is based on the existing approximate solution where a polynomial is used to approximate the concentration profile inside the particle. Diffusion in the electrolyte and the concentration polarization effect are simplified using the approximate solution based on parabolic profile approximation for the electrolyte concentration distribution. Especially, this model analyzes the mathematical description of the non-uniform reaction distribution effect inside the electrode, and an approximate solution of this effect is obtained by synthetically applying the volume average technique, approximated by the uniform reaction distribution situation, exponential profile approximation and the iterative calculation techniques. Thus the description of the non-uniform reaction distribution effect is successfully extended and the pore wall fluxes at the two current collector interfaces can be accurately predicted. Simulation results show that this model greatly improves the computational efficiency with little loss of accuracy.