A thermal energy storage unit filled with phase change material (PCM) can serve as a heat sink for the cooling of electronics with intermittent or periodic heat dissipation rates. The use of thermal conductive structures (TCS) is an effective method of improving the thermal performance of a PCM-based heat sink. In this paper, topology optimization is explored to develop a new class of TCS with a tree-like structure to enhance the thermal performance of a trapezoidal heat sink. The topology-optimized heat sink was then fabricated by Selective Laser Melting (SLM) using an aluminum alloy, AlSi10Mg, as the base powder. Experiments were performed to evaluate the thermal performance of the topology-optimized heat sink with the tree-like structure. In addition, a conventional longitudinal-fin heat sink of the same solid volume fraction (φ = 16.2%) and a heat sink without enhanced structure were also fabricated and experimentally investigated for comparison. Rubitherm RT-35HC paraffin wax was used as the PCM. Three different heat fluxes of 4.00 kW/m2, 5.08 kW/m2 and 7.24 kW/m2 were applied at the base of each specimen by a silicone rubber heater. The structure wall and the PCM temperatures were measured over time. Our results show that, for all heat rates tested, the topology-optimized heat sink was able to maintain a lower base temperature as compared to the fin-structure and the plain heat sinks. A thermal enhancement ratio (ε) is defined to evaluate the performance of the heat sinks with and without the use of PCM. From the experimental results, the highest ε value of 8.6 was achieved by the topology-optimized heat sink. These results indicate the better performance of the topology-optimized heat sink in dissipating heat as compared to the other specimens.