Melamine foam (MA) as an ultra-light porous foam is an ideal phase-change medium packaging material to prepare shape-stable phase change materials (ss-PCMs). In this paper, tetradecylamine (TDA) was used as a thermal energy storage medium and melamine foam was used as the container. The melamine covalently bonded multi-walled carbon nanotubes (MWCNTs) with azide polyacrylic acid (APAA) as an intermediate medium (MA-APAA-MWCNTs) was used to improve the thermal conductivity of melamine foam. Then, the surface of the skeleton of melamine foam/MA-APAA-MWCNTs composite was grafted with TDA by using polyacrylic acid chloride (PACl) as an intermediate medium to change the interaction between melamine foam and TDA. When the MA-APAA-MWCNTs loading was 8%, the thermal conductivity of the PCMs increased by 423%. Surface modification of melamine foam/MA-APAA-MWCNTs composite was used to prepare ss-PCMs, which shows a good encapsulation effect, large melting enthalpy (183.7 J/g), enhanced thermal conductivity and excellent cycle stability. The results presented in this work indicated that the resulting composite was promising candidate materials for building applications.