In this paper, a two-dimensional (2D) numerical study is presented on the melting process and heat transfer enhancement of a hybrid nanocomposite phase change material (HNCPCM) filled in a finned heat sink having a plate-pin structure. Hybrid nanoparticles of GNP-Cu with different volume fractions from 0.0 to 0.06 are dispersed inside the RT-35HC, used as a phase change material (PCM). The plate-pin heat sink has the volume fraction of 10% and constant fin height of 20 mm. The governing equations are solved through an unsteady approach using ANSYS-Fluent CFD code. The melt front of HNCPCM and dynamic temperature variations of heat sink temperature are evaluated at an input power level. The results showed that dispersing the hybrid nanoparticles improved the thermal conductivity and uniformity in the melting process of PCM compared to the pure PCM. The 0.02 volume fraction of GNP-Cu showed the higher melting time and optimum heat transfer rate. The addition of plate-pin heat sink reveals to lower the heat sink base temperature by extracting heat from the base of the heat sink towards the atmosphere resulting in maintains the electronic device in a comfortable operating temperature limit.