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Polyethylene glycol (PEG) is widely used as a phase change material (PCM) in thermal energy storage systems due to its high latent heat and chemical stability. However, practical application has been hindered by its low thermal conductivity and leakage issues. Therefore, developing shape-stable high thermal conductivity PCM is of great importance. In this study, new shape-stable composite PCM with high thermal conductivity and leak-prevention capabilities were designed. The porous carbon skeleton of diamond foam (DF) and dual-3D carbon nanotube-diamond foam (CDF) were prepared using the microwave plasma chemical vapor deposition method. The composite materials (DF/PEG and CDF/PEG) were produced by vacuum impregnation with PEG and skeletons. The results showed that CDF/PEG had the highest thermal conductivity, measuring 2.30 W·m−1·K−1, which is 707% higher than that of pure PEG. The employing of 3D networks of CNTs, which can improve the phonon mean free path in DF/PEG (1.79 W·m−1·K−1) while reducing phonon dispersion.The phonon vibration of dual-3D CDF plays an important role in heat transfer. PEG was physically absorbed and well-distributed in CDF, alleviating leakage of liquid PEG. The weight loss of CDF/PEG was only 25% at 70 °C for 120 s. Using CDF is an attractive and efficient strategy to increase the heat transfer of PEG and improve heat storage efficiency, alleviate the problem of poor shape-stability. [ABSTRACT FROM AUTHOR]