Highly spectrum-selective photodetectors have been proposed and fabricated from the i-ZnO/n-ZnO structure. In this structure, the n-ZnO layer acts as a "filter" that filtrates out the short-wavelength photons to ensure the high spectrum selectivity of the photodetector. Meanwhile, the i-ZnO layer acts as a "multiplier" in which photogenerated carriers can be multiplied via an impact ionization process. In this way, photodetectors with their response width of only 9 nm have been obtained, and the responsivity of the photodetectors can reach 4.91 A/W at -5 V bias, corresponding to a quantum efficiency of 1600%. The results reported in this paper may provide a general route to high-performance, highly spectrum-selective photodetectors.