A series of fatty acids/carbon nanotubes (CNTs) composite shape-stabilized PCMs were prepared through infiltration method by using the eutectic mixture of capric acid, lauric acid, and palmitic acid as phase change materials, multi-walled CNTs as a supporting material. Nitrogen adsorption-desorption curves and SEM images of composite shape-stabilized PCMs indicate that the eutectic mixture was effectively absorbed into the porous structure of the CNTs. DSC thermograms show that the composite fatty acids/CNTs possess good phase change behavior. And the latent heat of the sample absorbed with 80 wt% fatty acids can achieve 101.6 J g -1 in the melting process and its phase change temperatures and latent heat almost remain unchanged in 30 times of thermal cycling. Moreover, the thermal conductivity of the composite materials are significantly improved (up to 0.6661 W m -1 k -1 ) due to the addition of the highly thermal conductive CNTs.