A novel numerical model for simulating the behavior of lithium-ion batteries based on LiFePO4(LFP)/graphite is presented. The model is based on the modified Single Particle Model (SPM) coupled to a mesoscopic approach for the LFP electrode. The model comprises one representative spherical particle as the graphite electrode, and N LFP units as the positive electrode. All the SPM equations are retained to model the negative electrode performance. The mesoscopic model rests on non-equilibrium thermodynamic conditions and uses a non-monotonic open circuit potential for each unit. A parameter estimation study is also carried out to identify all the parameters needed for the model. The unknown parameters are the solid diffusion coefficient of the negative electrode (D-s,D-n), reaction-rate constant of the negative electrode (K-n), negative and positive electrode porosity (epsilon(n)&(n)), initial State-Of-Charge of the negative electrode (SOCn,0), initial partial composition of the LFP units (y(k,0)), minimum and maximum resistance of the LFP units (R-min&R-max), and solution resistance (R-cell). The results show that the mesoscopic model can simulate successfully the electrochemical behavior of lithium-ion batteries at low and high charge/discharge rates. The model also describes adequately the lithiation/delithiation of the LFP particles, however, it is computationally expensive compared to macro-based models.