Recycled aggregate base, usually utilized in permeable roadways, can be stabilized by geosynthetics to reduce rutting. However, the inclusion of geosynthetics would cause a magnified resilient behavior of the aggregate base under cyclic loading and the mechanism is still not well understood. In this study, cyclic triaxial tests were conducted to investigate the effect of the geosynthetic on the performance of the recycled aggregates. Results show that the resilient strains of aggregate samples stabilized by geosynthetics increased; correspondingly, the calculated loading/unloading moduli decreased and volumetric strains increased. However, a significant reduction of the cumulative plastic strains was observed. The main reason for such results is that the lateral confinement provided by geosynthetics was mobilized and caused the major principal stress to vary from the vertical direction to the lateral direction periodically along with the applied cyclic loading. This cyclic variation of the major principal stress would induce a cyclic shear action that causes the structural rearrangement of aggregates, leading to the dilation of samples. The major principal stress in the lateral direction during the unloading process results in a large vertical extension, which not only leads to a magnified resilient strain but also causes a reduced plastic strain.