Fatty alcohols have been identified as promising organic phase change materials (PCMs) for thermal energy storage, because of their suitable temperature range, nontoxicity and can be obtained from both natural and synthetic sources. Like all other organic PCMs, octadecanol (OD) as PCM suffers from low thermal conductivity (TC). In this work, to enhance its TC, it was grafted on the functionalized MWCNT and were used as a conductive filler to enhance overall thermal properties of OD in a composite PCM (CPCMs) structure. The OD/OD-g-MWCNT sample showed better dispersion within the composites and the presence of additional OD boosted the overall heat storage enthalpy compared to that of plane composite sample with OD/MWCNT. In a non-quantitative approach, it was observed that, any increase in grafting ratio of OD increases the heat storage enthalpy of the composites. The heat storage enthalpy of (267.7J/g) OD/OD-g-MWCNT(4:1)-5wt% composite PCM had reached very close to the heat storage enthalpy value of pure OD (269.3J/g), and much higher than that of OD/MWCNT-5wt% (234.5J/g). Champion sample i.e. OD/OD-g-MWCNT (4:1)-5wt%, showed good heat storage enthalpy, cycling performance, thermal stability and TC enhancement by 262.5%.