Alumina ($Al_2O_3$) nanoparticles with three different interface structures have been selected as reinforcement fillers for epoxy nanocomposite, that is surface untreated $Al_2O_3$ nanoparticles, ${gamma}$-aminopropyl-triethoxysilane modified $Al_2O_3$ nanoparticles ($Al_2O_3$-APS), and hyperbranched aromatic polyamide grafted $Al_2O_3$ nanoparticles ($Al_2O_3$-HBP). The interface structures of the $Al_2O_3$ nanoparticles were characterized by X-ray diffraction and atomic force micrographs. Our studies reported the influence of the interface structure of $Al_2O_3$ nanoparticles on the morphology and dielectric properties of epoxy nanocomposites. It was found that the incorporation of the $Al_2O_3$-APS and $Al_2O_3$-HBP nanoparticles not only improved the dispersion of the nanoparticles in the epoxy matrix, but also enhanced the glass transition temperatures ($T_gs$) and largely influenced the dielectric properties of the epoxy nanocomposites as compared with the nanocomposites filled with the surface untreated $Al_2O_3$ nanoparticles. The improvement of $T_gs$, volume resistivity, dielectric strength, and the reduction of dielectric loss could be attributed to the good dispersion and special interface structure of the $Al_2O_3$ nanoparticles in the epoxy matrix.