Graphene was known as the material that owning many superiority properties and high thermal conductivity. Thermal conductivity of single-layer graphene was up to 5200 W/mK (compared to the thermal conductivity of Carbon nanotubes 2000 W/mK and Silver 410 W/mK). This had suggested that graphene is the most potential material for heat dissipation applications for electronic devices, such as a computer microprocessor, high power LED... To enhance the dispersion of the GNPs silicone matrix, we were functionalized graphene nanoplatelets (GNPs) with carboxyl (-COOH) groups. The silicone thermal greases containing GNPs were prepared by High-Energy Ball Milling method (8000D Mixer /Mill). The results of SEM, FTIR, Raman showed the presence of the carboxyl groups in GNPs and GNPs uniform dispersion dispersed in grease. The results of thermal conductivity from Transient Hot Bridge THB-100 showed that thermal conductivity enhancement was up to 234 % with Gr-COOH 1.0 vol.%. Thermal grease is used as a thermal interface material to coolants for Intel Core i5 processor. The results of thermal dissipation efficiency shown the saturation temperature of the processor using thermal grease containing 1.0 vol.% Gr-COOH decreased 4℃, compared to the silicone grease.