In this study, epoxy shape-memory polymer (ESMP) was infiltrated into the scaffolds of vertically aligned carbon nanotubes (CNTs) array grown by chemical vapor deposition (CVD). In the fabricated CNTs array/ESMP nanocomposite, the CNTs interconnected with each other and a three-dimensional (3D) network of the CNTs was formed. As a result, both thermal conductivity and electrical conductivity of the CNTs array/ESMP nanocomposite were higher than the random CNTs/ESMP composite fabricated by conventional high-speed mechanical stirring. In the random CNTs/ESMP composite, the CNTs aggregated seriously in the matrix. Along the CNTs axis, The CNTs array/ESMP nanocomposite showed a higher modulus and hardness than the random CNTs/ESMP composite, as revealed by nanoindentation tests. Under microwave radiation, the temperature of the CNTs array/ESMP nanocomposite increased more rapidly than pristine ESMP and the random CNTs/ESMP composite. Consequently, the CNTs array/ESMP nanocomposite showed a faster shape recovery speed compared with pristine ESMP and the random CNTs/ESMP composite in their microwavetriggered shape memory behaviors. Especially, the CNTs array/ESMP nanocomposite can recover the deformation fully in response to as low as 60 W microwaves. The presented CNTs array/ESMP nanocomposite with improved mechanical property and fast responses to low-power microwaves may find potential applications in smart devices.