Nanogap nowadays is fascinating in surface conduction electron-emitters (SCEs) for electron sources of the flat panel displays (FPDs). Surface conduction electron-emitter display (SED) is one of new type FPDs based on the SCEs. The nanogap fabricated by focused ion beam was studied, but the extremely narrow fissure complicated its fabrication. Palladium hydrogenation nanogaps have thus been proposed as a novel surface conduction electron-emitters for it low turn-on voltage, high emission current, high focused capability, and high emission efficiency. In this work, we investigate effects of nanogap separation width of the palladium hydrogenation nanogaps on the field emission efficiency using a finite-difference time domain particle-in-cell simulation method. The result of this study shows as the gap width increases, the field emission efficiency grows due to the larger space allows the particles attracted to the anode plate instead of attracting by the opposite electrode. Moreover, the study shows the better emission efficiency can be achieved under wider gap width, which reduces the difficulty of the fabrication.