In this study, a series of poly(ethylene glycol) (PEG)/unsaturated polyester resin (UPR)/graphene nanoplates (GNPs) form-stable PCMs (FS-PCMs) were prepared via a simple melt blending method. In this composite, PEG was used as the phase change material for thermal storage, UPR was introduced as a supporting material to prevent the leakage of melted PEG during the phase change transition and the GNPs were selected as conductive fillers to enhance the thermal conductivity of the polymer-based FS-PCMs. The test results demonstrate that the FS-PCMs exhibit an outstanding form-stable performance because of the cross-linked spatial network of UPR. According to the FT-IR and XRD results, no new chemical bonds form among PEG, UPR and the GNPs. The results obtained from TGA and DSC show that the composites possess an excellent thermal stability and a high energy storage density. Moreover, it is also found that the incorporation of GNPs remarkably enhances the thermal conductivity of the prepared FS-PCMs.