Jet impingement is a technique for removing heat efficiently. A liquid jet impingement on a cone heat sink was investigated numerically to explore the effect of filet profiles at the top and bottom edge of conical protuberances on fluid flow and heat transfer. An adopted turbulence model was validated through an experiment as described in the literature. Numerical results of pressure coefficient and Nusselt number were obtained for cases with and without filet profiles for variable jet Reynolds numbers and conical angles. Results showed that the flow and heat transfer of conical protuberances with small tip filet profiles are similar to that of the original cone. Pressure coefficient curves are similar to that of convex surfaces, and the average heat transfer slightly increases when the radius of the tip filet profiles exceeds 1 mm. A small filet profile of a conical bottom edge can improve the average Nusselt number. A secondary jet that enhanced the overall heat transfer was demonstrated, and the heat transfers of convex surfaces, as the comparison, with small angles were enhanced in most cases.