In this work, a planar electron emission device based on a graphene/hexagonal boron nitride (h-BN)/n-Si heterostructure is fabricated to realize highly monochromatic electron emission from a flat surface. The h-BN layer is used as an insulating layer to suppress electron inelastic scattering within the planar electron emission device. The energy spread of the emission device using the h-BN insulating layer is 0.28 eV based on the full-width at half-maximum (FWHM), which is comparable to a conventional tungsten field emitter. The characteristic spectral shape of the electron energy distributions reflected the electron distribution in the conduction band of the n-Si substrate. The results indicate that the inelastic scattering of electrons at the insulating layer is drastically suppressed by the h-BN layer. Furthermore, the maximum emission current density reached 2.4 A/cm(2), which is comparable to that of a conventional thermal cathode. Thus, the graphene/h-BN heterostructure is a promising material for planar electron emission devices to obtain a highly monochromatic electron beam and a high electron emission current density.