In this study, novel kinds of form-stable composite phase change materials (FS-CPCM) were prepared by the vacuum impregnation method. In the FS-CPCM, lauric acid (LA) was the PCM, and LA was grafted on the surface of graphene aerogel (GA) by an esterification reaction and reduction process to prepare supporting material and increase the thermal conductivity of the FS-CPCMs. The microstructure, thermal storage properties, thermal conductivity and light-to-heat conversion of the FS-CPCMs were investigated. Scanning electron microscopy and Fourier transform infrared spectroscopy were used to demonstrate that the LA was encapsulated effectively in the porous structure of the LA-GA, and the LA/LA-GA FS-CPCMs were prepared successfully. X-ray diffractometer results confirmed that the crystallization of the LA/LA-GA FS-CPCM was better than that of LA/GA FS-CPCM. Thermal conductivity analyses indicated that the thermal conductivities of the LA/LA-GA-1 FS-CPCMs increased 352.1% and 32.6% compared with the conductivities of LA and LA/GA FS-CPCM, respectively. Differential scanning calorimetry results confirmed that the LA/LA-GA-1 FS-CPCM possess good phase change behavior, low undercooling and excellent thermal cycling stability. The melting enthalpy and freezing enthalpy could reach 207.3 J/g and 205.8 J/g, respectively, and the LA/LA-GA FS-CPCM exhibited good thermal reliability and stability. Furthermore, the LA/LA-GA FS-CPCM had excellent photon absorption and the highest efficiency in terms of light-to-heat conversion of 80.6%. Such good performances demonstrate the LA/LA-GA FS-CPCM's potential for use in solar energy storage systems.