Shape memory polymers (SMPs) have broad prospects in many fields such as medical devices and aerospace and so on due to their large shape variable, excellent shape recovery performance, and rich stimulation methods. In this paper, the carboxylated multiwall carbon nanotubes (MWCNT) were used as photothermal conversion filler on the basis of thermally initiated polycaprolactone (PCL) crosslinking with diisopropylbenzene peroxide (DCP). The carboxylated MWCNT/PCL photothermal response shape memory materials were prepared by melt blending method. The photothermal conversion properties, shape memory properties and mechanical properties of the composites were studied. The results show that the addition of carboxylated MWCNT makes the material have the characteristics of light response and improves the mechanical properties. When the mass fraction of DCP and the carboxylated MWCNT is 1.5% and 1% respectively, the shape fixation rate and shape recovery rate of the material are the best, which are 99.37% and 98.53%, respectively. The material can restore its original shape within 30 s under near-infrared light irradiation, showing excellent shape memory performance. Compared with the uncrosslinked composite, the tensile strength is increased by 81.85% from 15.37 MPa to 27.85 MPa, while the elongation at break is decreased by 6.12% from 1046.5% to 982.48%.