High thermal conductivity, large latent heat of fusion and good shape stability are all required for practical applications in phase change composites. Lightweight cellulose/GNP aerogels are fabricated by combining defect-free graphene nanoplatelets (GNPs) and microcrystalline cellulose. Defect-free GNPs with a high intrinsic thermal conductivity are fabricated by annealing thermal exfoliation graphite oxide at high temperature of 2200 oC to remove their oxygen-containing groups and heal their structure defects, and used as thermally conductive fillers to improve the thermal conductivity. Cellulose network was used as a supporting skeleton to supply a high mechanical strength. The resultant aerogels possessing highly porous but strong three-dimensional networks benefit the encapsulation of polyethylene glycol (PEG) and prevent the leakage of PEG above its melting point. Phase change composites are prepared by vacuum-assisted impregnating of PEG into the cellulose/GNP aerogels, which exhibit high thermal conductivity, good shape stability and high latent heat of fusion. Even compressed upon the melting point of PEG, the phase change composites keep their shapes stable without any leakage. Thermal conductivity of composites increase with the graphene loading. With only 5.3 wt% of GNPs, the composite exhibits a high thermal conductivity of 1.28 W∙m-1∙K-1, 481 % higher than that of the composite without GNPs. The highly porous cellulose network and the low loading of highly thermally conductive GNPs are responsible for the high loading of PEG in the composite with a large latent heat of fusion of 156.1 J∙g-1.