The continuous increase in greenhouse gas emissions and the depletion of the fossil fuels are the main driving forces behind efforts to more effective utilization of renewable energy from various sources. Energy storage systems not only improve the performance and reliability of energy systems but also provide the potential to attain energy savings and reduce the mismatch between supply and demand of energy, which in turn reduce the impact on environment. Latent heat thermal energy storage realized by using phase change materials (PCMs) is one of the most effective techniques for storing thermal energy. Polyethylene glycol (PEG) is considered a very promising solid–liquid organic PCM due to its high phase change enthalpy, chemical and thermal stability, biodegradation, non-toxicity, non-corrosiveness, low vapor pressure and suitable melting temperature. However, two intrinsic disadvantages associated with PEG are the low thermal conductivity which severely limited the rate of heat absorbing and releasing, and the leakage of liquid phase above the melting temperature. In current work, graphene oxide (GO) sheets were introduced as supporting materials to stabilize the melted PEG during the solid–liquid phase change process and exfoliated graphene nanoplatelets (xGnPs) were used as conductive fillers to improve the thermal conductivity. The structural properties and phase change behaviors of the PEG/GO/xGnPs composites were investigated by means of various characterization techniques. The results showed that no leakage of PEG occurred till a temperature much higher than the melting point. Meanwhile, the thermal conductivity of the form-stable composite PCM was increased by ca. 400%. The shape-stable PCM with high thermal conductivity presents a high heat storage capacity due to low content of fillers and excellent thermal reliability within at least 200 melting/freezing cycles.