Given the rapid developments in modern devices, there is an urgent need for shape-memory polymer composites (SMPCs) in soft robots and other fields. However, it remains a challenge to endow SMPCs with both a reconfigurable permanent shape and a locally reversible shape transformation. Herein, a dynamic cross-linked network was facilely constructed in carbon nanotube/ethylene vinyl acetate copolymer (CNT/EVA) composites by designing the molecular structure of EVA. The CNT/EVA composite with 0.05 wt % CNT realized a steady-state temperature of ∼75 °C under 0.11 W/cm2 light intensity, which gave rise to remote actuation behavior. The dynamic cross-linked network along with a wide melting temperature offered opportunities for chemical and physical programming, thus realizing the achievement of the programmable three-dimensional (3D) structure and locally reversible actuation. Specifically, the CNT/EVA composite exhibited a superior permanent shape reconfiguration by activating the dynamic cross-linked network at 140 °C. The composite also showed a high reversible deformation rate of 11.1%. These features endowed the composites with the capability of transformation to 3D structure as well as locally reversible actuation performance. This work provides an attractive guideline for the future design of SMPCs with sophisticated structures and actuation capability.