Lithium-ion (Li-ion) cells degrade after repeated cycling and the cell capacity fades while its resistance increases. Degradation of Li-ion cells is caused by a variety of physical and chemical mechanisms and it is strongly influenced by factors including the electrode materials used, the working conditions and the battery temperature. At present, charging voltage curve analysis methods are widely used in studies of battery characteristics and the constant current charging voltage curves can be used to analyze battery aging mechanisms and estimate a battery's state of health (SOH) via methods such as incremental capacity (IC) analysis. In this paper, a method to fit and analyze the charging voltage curve based on a neural network is proposed and is compared to the existing point counting method and the polynomial curve fitting method. The neuron parameters of the trained neural network model are used to analyze the battery capacity relative to the phase change reactions that occur inside the batteries. This method is suitable for different types of batteries and could be used in battery management systems for online battery modeling, analysis and diagnosis.