Based on the experimentally determined microstructure of a lithium ion battery (LIB) cathode electrode using X-ray nano-CT technology, a three dimensional simulation framework of galvanostatic discharge with finite volume method is presented. The tomography data were used to evaluate the homogeneity of porosity and tortuosity of the electrode. With this approach, galvanostatic discharge processes at different C rates were simulated and the local effects in the LIB cathode electrode during discharge processes were investigated. The spatial distribution of physical and electrochemical properties in the microsturcture of the cathode electrode, such as concentration, current density, open circuit potential (OCP), overpotential and intercalation reaction rate was revealed in this paper. The simulation results show that the distributions of those properties are very different from the results based on the pseudo two dimensional model. The physical and electrochemical properties distribute in a wider range due to the structure inhomogeneity, which may have a negative impact on LIB performance, especially at large discharge rates.Rechargeable lithium-ion batteries (LIBs) have dominated the power source market for portable electronic devices for many years. Recently, they have attracted a lot of interests in automobile applications due to their relatively high energy and power densities. For instance, LIBs have been used in electric (Nissan Leaf) or plug-in hybrid electric cars (Chevy Volt). However, significant challenges still exist in LIBs, such as capacity fade, unpredicted safety issues, and fast charging. In order to improve battery performance, a lot of effort has been done toward the development of new anode and cathode materials. 1-4 Besides the electrode material properties, the structure of electrodes also plays a critical role in determining the performance of a LIB. 5,6 The microstructure of the active materials forms the boundary for the physical and electrochemical processes within the electrode, such as lithium ion transportation, heat generation, side reactions, phase transformation, and inner stresses. The response of LIBs could be determined by the electrode microstructure especially in the application of high energy and power densities. 7 In order to address the challenges and design better LIB electrodes, fundamental understandings of the physical and electrochemical processes inside a battery during charge and discharge processes are necessary.Mathematical modeling and numerical simulation have been proven to be effective ways to reveal both global and local phenomena that occur in LIB electrodes. Combined with experimental validations, they can give valuable insights into the principles of the LIB performance. To this end, comprehensive mathematical models and variant numerical methods have been developed to simulate the behavior of LIBs and reveal the effect of the microstructure on the performance of LIBs. For instance, Doyle et al. developed a mean field method which incorporates the electrode mi...