Recently, CDIs with intercalation electrodes have attracted extensive attention due to their high ion storage capacity. A lattice Boltzmann (LB) model is developed to investigate the desalination process of intercalation CDIs on the pore-scale level. Numerical treatments on the boundary conditions at pore/particle interfaces are proposed to describe the ion and charge transfer across the interfaces. After validation of the LB model, pore-scale simulation is performed to reveal desalination dynamics of intercalation CDI under the constant current condition, and effects of current density, porosity and flow configuration on the desalination performance are investigated. Simulation results show that spatial distributions of concentration and intercalation degree within the porous electrode exhibit highly nonuniform and nonlinear characteristics during the adsorption process. The average salt adsorption rate (ASAR) can be improved by increasing the current density but with the sacrifice of reduction in the salt adsorption capacity (SAC). The SAC increases with the decrease of electrode porosity mainly due to the increment of time in the adsorption cycle, while the ASAR maintains unchanged for different porosities. Compared with the conventional flow-by configuration, the configuration with double flow channels is desirable for alleviating the concentration polarization across the electrode and thus improving the SAC.