Li-ion battery is a complicated distributed parameter system that can be described precisely by field theory and partial differential equations. In order to reduce the calculation amount and the solution difficulty, a distributed parameter system is often described by ordinary differential equation model during the design and the analysis. As a result, systemic error is caused, and the reliability of the system model is reduced. The rechargeable Li-ion batteries are widely used in many fields because of their excellent properties. The research on the modeling and failure monitor of Li-ion battery can evaluate its working state, and improve the security during its servicing. Li-ion battery system is regarded as a distributed parameter system in this paper. Single particle model is a simplification of a Li-ion battery under a few assumptions. According to the measured data, single particle model can be used for estimating the parameter at a fast simulation speed. Li-ion battery model based on partial difference equations and single particle model is proposed to detect the failure and evaluate the working state of Li-ion battery system. Lithium ion concentration is an unmeasurable distributed variable in the anode of Li-ion battery. The failure monitor system can track the real-time Li ion concentration in the anode of Li-ion battery, calculate the residual which is the difference between the measured value and the ideal value. A failure can be judged when the residual is beyond a predefined failure threshold. A simulation example verifies that the accuracy and the effectiveness of Li-ion battery failure monitor system based on parabolic partial difference equations and single particle model is reliable.