We report a remarkable improvement of photoluminescence from ZnO-core/a-SiN(x):H-shell nanorod arrays by modulating the bandgap of a-SiN(x):H shell. The a-SiN(x):H shell with a large bandgap can significantly enhance UV emission by more than 8 times compared with the uncoated ZnO nanorods. Moreover, it is found that the deep-level defect emission can be almost completely suppressed for all the core-shell nanostructures, which is independent of the bandgaps of a-SiN(x):H shells. Combining with the analysis of infrared absorption spectrum and luminescence characteristics of NH(x)-plasma treated ZnO nanorods, the improved photoluminescence is attributed to the decrease of nonradiative recombination probability and the reduction of surface band bending of ZnO cores due to the H and N passivation and the screening effect from the a-SiN(x):H shells. Our findings open up new possibilities for fabricating stable and efficient UV-only emitting devices.