Thermal management in devices directly affects their performance, but it is difficult to apply conventional cooling methods such as the use of cooling liquids or fans to micro devices owing to the small size of micro devices. In this study, we attempted to solve this problem by employing a heat sink fabricated using copper with porous structures consisting of single-layer graphene on the surface and graphene oxide inside the pores. The porous copper/single-layer graphene/graphene oxide composite (p-CuGrGO) had a porosity of approximately 35%, and the measured pore size was approximately 10 to 100 µm. The internal GO was reduced at a temperature of 1000 ℃. On observing the heat distribution in the structure using a thermal imaging camera, we could observe that the p-CuGrGO was conducting heat faster than the p-Cu, which was consistent with the simulation. Furthermore, the thermal resistance of p-CuGrGO was lower than those of the p-Cu and pure Cu. When the p-CuGrGO was fabricated into a heat sink to mount the light emitting diode (LED) chip, the measured temperature of the LED was 31.04 ℃, which was less than the temperature of the pure Cu of 40.8 ℃. After a week of being subjected to harsh conditions, p-CuGrGO observed 95.24% light intensity, but the light intensity of pure Cu decreased to 66.04%. The results of this study are expected to be applied to micro devices for their effective thermal management.