Phase change material (PCM)-based heat sinks have the potential to provide reliable thermal management for electronic devices. However, the low thermal conductivity of PCMs hampers their use in large-volume or high-power devices. Embedding a PCM in a porous matrix is an efficient method for enhancing heat dissipation in a passive cooling application. In this study, the copper fibers with ample antler microstructures on their surface were first introduced into the phase change heat transfer enhancement technology. The enhanced heat transfer performance of a PCM embedded in a porous metal fiber sintered felt (PMFSF) was experimentally investigated. Paraffin/PMFSF composite PCM (MF-PCM) was prepared, and three types of heat sinks (filled with MF-PCM, filled with paraffin, and empty) were tested under four power levels. The effect of the porosity was also investigated. It was found that the addition of PMFSF enhanced heat transfer to the PCM, leading to lower heat source temperature. The improvement of heat transfer by MF-PCM is more evident under larger heat flux. Before melting is completed, lower heat source temperature and temperature gradient is achieved for the heat sink with low porosity, while longer duration of temperature control region is achieved in the case of the heat sink with the higher porosity. The time-averaged effective thermal resistance of the heat sink with paraffin is higher than that of the heat sinks with MF-PCM. All these results show the enormous potential of using PMFSF to replace metal foams, thus offering a new porous metal matrix to enhance the thermal conduction of PCMs.