We calculate the scattering cross section for inverse compton scattering in curvedrnspacetime in the presence of strong magnetic eld. An approximate solution ofrnDirac equation in a spatially rnat RW spacetime has been established. And itsrnsolution in Friedman universe is also discussed. The scattering cross section wernfound contains the expanision parameter of the expanding universe and this makesrnmain di erence from the special relativistic results. We investigate the role ofrnthe expanission parameter to the scattering cross section of the inverse comptonrnscattering