The dynamic ion transport and adsorption process has been numerically investigated for porous electrode used in the capacitive deionization, which is a new desalination technology in recent years. To identify the complex kinetics of the process, Navier-Stokes equations and Poisson-Nernst-Planck equations are solved in an iteratively coupled manner based on lattice Boltzmann method. The proposed numerical model is validated and then used to investigate the transient ion adsorption at pore scale level. The results show that particle surface potential directly determines the ion adsorption amount. Inlet velocity does not affect the final ion adsorption amount, but changes the time to reach the final steady state. The effects of porous structures on the ion adsorption process are discussed in terms of structures of electric double layers and permeability. Under the present simulation condition, the porous structure S2 with a moderate particle aggregation degree shows the best capacitive deionization performance.