Neutrino-dominated accretion flows (NDAFs) are one of the important MeV neutrino sources and significantly contribute to the cosmic diffuse neutrino background. In this paper, we investigate the spectrum of the diffuse NDAF neutrino background (DNNB) by fully considering the effects of the progenitor properties and initial explosion energies based on core-collapse supernova (CCSN) simulations, and estimate the detectable event rate by the Super-Kamiokande detector. We find that the predicted background neutrino flux is mainly determined by the typical CCSN initial explosion energy and progenitor metallicity. For the optimistic cases, in which the typical initial explosion energy is low, the diffuse flux of the DNNB is comparable to the diffuse supernova neutrino background, which might be detected by upcoming larger neutrino detectors, such as Hyper-Kamiokande, the Jiangmen Underground Neutrino Observatory, and the Deep Underground Neutrino Experiment. Moreover, the strong outflows from NDAFs could dramatically decrease their contribution to the neutrino background.