During the formation of cosmic web, collisionless shock waves are produced around and inside the substructures. In these shock waves electrons and ions are accelerated to such high energies that they can produce gamma rays in several ways. Many authors have studied the contribution of shock-induced radiation to the cosmic gamma-ray background. However not all the important physical processes are included in their calculation. By considering more complete physical process, we re-investigate the problem. In our model, the energy distribution of the cosmic rays (CRs) are calculated by widely accepted diffusive shock acceleration model, both primary and secondary CR electrons are included, both inverse Compton scattering and bremsstrahlung process are considered. The difference of the results are discussed.