The application and progress of calculation and simulation in the field of metal corrosion are summarized in this paper, which provide a cross-scale method combined with first-principles and finite element calculation to investigate the behavior and mechanism of Al and its alloys. We have carried out the calculations of the adsorption of O2 and H2O on Al surface to study the forming mechanism of passive film. The pitting initiation was studied by the interaction between Cl- and passive film using first-principles calculations, which was proved that the pitting initiation tended to Cl- adsorption induced oxide thinning. The adsorption, solution and diffusion of H atom was performed along Al (111) surface to obtain the most stable adsorption and solution site and the diffusion energy barrier. A grain boundary (GB) and grain models were constructed to characterize the solution and diffusion of H atom. The strength of GB characterized by its cohesive energy was calculated by first-principles method, which decreased with the increasing H concentration segregated in GB. The cohesive energies were input into cohesive finite element calculations as the fracture energies to simulate the intergranular cracking, which was a cross-scale study. The application of the cross-scale approach is very efficient for investigating the evolution of hydrogen induced intergranular cracking. The work of this study provides a scheme using a cross-scale calculation from atomic scale to macro-scale to study the atmospheric corrosion behavior and mechanism of metals.