Extending the two-dimensional topology of wireless networks to the three-dimensional (3D) structure has recently been recognized as a revolutionary breakthrough for the next generation of wireless communication networks. As revealed in the literature, dispatching the unmanned aerial vehicle (UAV) assisted base-station (UBS) can fill in the coverage holes as the low energy-efficiency (EE) BSs on the ground are switched off. De facto, properly deploying the UBSs can further enlarge the flexibility of the user handover and exchange procedures in the sleep strategy. Thus, in this paper, we propose a low-complexity UBS-assisted sleep strategy for the small-cell network (SCN). Verified by the simulation results, it is found that deploying a proper number of capable UBSs can remarkably raise the EE for the 3D SCNs.