This work proposes a facile method to greatly improve the thermal conductivity, while retaining the low electrical conductivity, of epoxy composites by incorporating boron nitride nanoparticles (BNNPs). BNNPs were surface modified by noncovalent functionalization with 1-pyrenebutyric acid to obtain a stable aqueous BNNP dispersion. The functionalized BNNPs (f-BNNPs) were characterized by X-ray photoelectron spectroscopy (XPS), Fourier transformation infrared (FTIR), and thermogravimetric analysis (TGA). The f-BNNPs were found to yield the f-BNNP/epoxy composites showing a homogeneous dispersion of BNNPs and a strong BNNP-epoxy interfacial adhesion. The f-BNNP/epoxy composites with 10 wt.% f-BNNPs exhibited a high thermal conductivity of 1.58 W m−1 K−1 and a low electrical conductivity of 2.5 × 10−16 S m−1. The present f-BNNP/epoxy composites can be potentially utilized in electronic packaging that requires electronic insulators with high thermal conductivity.