Carbon nanotubes (CNTs) were grafted with polyhydric alcohols (octanol, tetradecyl alchohol and stearyl alcohol) after acidification. The composite phase change materials (PCMs) were prepared with grafted CNTs and paraffin. The grafted CNTs were characterized with Transmission Electron Micrograph (TEM), X-ray Diffractometer (XRD), Fourier Transform Infrared Spectroscopy (FTIR) and Thermogravimetric analyzer (TG). Hot disk method was employed to measure the thermal conductivity of composite PCMs. The results showed that polyhydric alcohols were grafted onto CNTs. The graft ratio was 38% for the CNTs grafted with stearyl alcohol. The grafted CNTs were shorter than CNTs and the dispersibility of grafted CNTs was better than that of CNTs. The thermal conductivity of grafted CNTs/paraffin composite PCMs was higher than that of pristine CNTs/paraffin composite PCMs. (C) 2014 Elsevier Ltd. All rights reserved.