Lithium-ion batteries have the characteristics of high energy densities, high operate voltage, large output power, and high cycle life. In addition, the low self-discharge rates and the long storage life, making lithium-ion batteries well suited for 3C applications and stationary applications. The mathematical modeling of lithium-ion battery has been developed in this study, based on electrochemistry, combined with thermodynamics, transport phenomena, ohm’s law, and electrochemical kinetics, the model systems was simulated by computer-aided software engineering. The one-dimensional (flow) model was solved by COMSOL 4.3a software, and the Butler–Volmer equation was solved by MATLAB. The results were compared to the P2D model in COMSOL and the experiments which were performed on CR2032 Li-ion cell with various negative electrode materials (KS-6 graphite, Silicon, C-coated Si, and KS-6/Si). Two different approaches have employed to model the insertion of lithium ions into an negative electrode particle: the Fick's second law and the nonlinear diffusion model considering the vacancy effect. Then, the model system was then scaled up to a cylindrical 18650 lithium cobalt oxide cell. By changing the manufacturing parameters, various effects on the batteries performance would be investigated. Using small particles, increasing the diffusion coefficient of lithium in solid state, and less electrode porosity could increase the discharge capacity. The model involving SEI formation has been developed to simulate the capacity fade of 18650 Li-ion batteries in first few cycles. The largest capacity losses due to solid electrolyte interphase (SEI) growth have been found in the first cycle, and were steady in the next several cycles.