A hybrid heat sink concept which combines passive and active cooling approaches is proposed. The hybrid heat sink is essentially a plate fin heat sink with the tip immersed in a phase change material (PCM). The exposed area of the fins dissipates heat during periods when high convective cooling is available. When the air cooling is reduced, the heat is absorbed by the PCM. The governing conservation equations are solved using a finite-volume method on orthogonal, rectangular grids. An enthalpy method is used for modeling the melting/re-solidification phenomena. Results from the analysis elucidate the thermal performance of these hybrid heat sinks. The improved performance of the hybrid heat sink compared to a finned heat sink (without a PCM) under identical conditions, is quantified. In order to reduce the computational time and aid in preliminary design, a one-dimensional fin equation is formulated which accounts for the simultaneous convective heat transfer from the finned surface and melting of the PCM at the tip. The influence of the location, amount, and type of PCM, as well as the fin thickness on the thermal performance of the hybrid heat sink is investigated. Simple guidelines are developed for preliminary design of these heat sinks.