To clarify the influence of large shear strain on the cyclic behavior on liquefiable granular materials, a series of undrained cyclic simple shear simulations were carried out by utilizing 3D discrete element method (DEM). The amplitudes of the cyclic shear strain loaded on specimens range from 0.3% to 100%. The results show that when the cyclic shear strain loaded exceeds a certain amplitude, both the loose and the dense specimens exhibited high energy absorption properties, positive dilatancy characteristics, and non-liquefaction behaviors. This phenomenon might be caused by the uneven spatial distribution of particles during cyclic shear loadings. In addition, the liquefiable cyclic shear strain amplitude range is affected by the density and particle size of specimens.