The leakage of the liquid phase above the melting point and the low thermal conductivity of phase change materials (PCMs), are the major barriers that currently prevent the practical applications of organic PCMs. In this work, a novel supporting material with mutual interpenetrating network structure was developed by the heterogeneous decorations of Cr-MIL-101-NH2 metal-organic frameworks (MOFs) nanoparticles on the surfaces of carbon nanotubes (CNTs). PCMs, absorbed by capillary force of porous structure and anchored by hydrogen bond interaction of amino groups, were stabilized by the MOFs nanoparticles. The close integration between CNTs and MOFs nanoparticles was conductive to the construction of three-dimensional (3D) and mutual interpenetrating network structured supporting material, which provided continuous heat transfer paths, increased mean free paths for phonons transmission and promoted effectively the reduction of interfacial thermal resistance between the PCM molecules and supporting materials. The thermal conductivity of PEG2000/CNT@ Cr-MIL-101-NH (2) shape-stabilized PCM composite was improved by 100.9% over PEG2000/Cr-MIL-101-NH2 PCM composite. Furthermore, the obtained PEG/CNT@ Cr-MIL-101-NH2 PCM composite showed large phase change enthalpy, good chemical stability and excellent thermal cycling stability.