Poor thermal conductivity and easy leakage in molten state into the surrounding of the thermal energy storage (TES) system are two major problems of organic phase change materials (OPCMs). This study focuses on the heat conduction enhancement and leakage-proof of the OPCM and a novel shape-stabilized OPCM with decyl alcohol (DA) as TES material, expanded graphite (EG) and nanoparticles as additives is developed. The optimal mass fraction of the porous EG, which serves as the shape-stabilizer and heat conduction enhancer, is determined to be 9% through vacuum drying method. Five different kinds of nanoparticles are selected to further improve the thermal conductivity. The experimental results suggest that the composite PCM DA/MgO/EG possesses the highest thermal conductivity, with a value of 1.873 W/(m·K), which is significantly increased by 11.570 times comparing to pure DA and 1.010 times higher than that of DA/EG. The mechanism of strengthening thermal conductivity by the coupling effect of EG and nano additives is revealed. According to DSC tests, the melting temperature and the melting enthalpy of the ternary composite PCM DA/MgO/EG are 1.1 °C and 194.6 J/g, respectively. The effect of additives on the phase transition temperature and enthalpy of PCMs is also investigated. Depending on the cyclic stability experiments, after 300 charging-discharging cycles, both the phase transition temperature and the melting latent heat of DA/MgO/EG have little change by comparison with those of uncirculated composites, which indicates excellent thermal stability of the material. Finally, the applicability of DA/MgO/EG composite is explored by cold insulation experiment. Overall, the composite in this work has promising prospects in cold chain logistics.