We modified the Bean critical-state model by taking into consideration the surface barrier and the lower critical field of type-II superconductors. In the framework of this modified Bean critical-state model, we have calculated the initial magnetization curves and full hysteresis loops for an infinitely long cylinder immersed in an external ac field superimposed on a dc bias field. Through the computed M(H) curves, we give some discussion on the effect of A H and H_c1 to the initial magnetization and the temperature dependence of hysteresis loops of type-II superconductors.