Thermal management has become a critical challenge in electronics and portable devices. To address this issue, polymer composites with high thermal conductivity (TC) and low dielectric property are urgently needed. In this work, we fabricated perfluoroalkoxy (PFA) composite with high anisotropic TC and low dielectric constant by aligning boron nitride nanosheets (BNNs) via hot pressing. We characterized the thermal stability, microstructure, in-plane and through-plane TCs, heat dissipation capability, and dielectric property of the composites. The results indicate that the BNNs–PFA composites possessed good thermal stability. When the BNNs content was higher than 10 wt %, the BNNs were well layer aligned in the PFA matrix, and the composites showed obvious anisotropic TC. The in-plane TC and through-plane TCs of 30 wt % BNNs–PFA composite were 4.65 and 1.94 W m−1 K−1, respectively. By using the composite in thermal management of high-power LED, we found that alignment of BNNs in composite significantly improves the heat dissipation capability of composite. In addition, the composites exhibited a low dielectric property. This study shows that hot pressing is a facile and low-cost method to fabricate bulk composite with anisotropic TC, which has wide applications in electronic packaging.