Inspired by the microstructures of naturally layered and highly oriented materials, such as natural nacre, we report a thermally conductive polymer composite that consists of epoxy resin and AlO platelets deposited with silver nanoparticles (AgNPs). Owing to their unique two-dimensional structure, AlO platelets are stacked together via a hot-pressing technique, resulting in a brick-and-mortar structure, which is similar to the one of natural nacre. Moreover, the AgNPs deposited on the surfaces of the AlO platelets act as bridges that link the adjacent AlO platelets due to the reduced melting point of the AgNPs. As a result, the polymer composite with 50 wt % filler achieves a maximum thermal conductivity of 6.71 W m K. In addition, the small addition of AgNPs (0.6 wt %) minimally affects the electrical insulation of the composites. Our bioinspired approach will find uses in the design and fabrication of thermally conductive materials for thermal management in modern electronics.