We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state ( EOSs ) modeled by piecewise polytropes . We focus , in particular , on the dependence of the gravitational waveform at the merger stage on the EOSs . The initial conditions are computed in the moving-puncture framework , assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field . For a small mass ratio of the binaries ( e.g. , M _ { BH } / M _ { NS } = 2 , where M _ { BH } and M _ { NS } are the masses of the black hole and neutron star , respectively ) , the neutron star is tidally disrupted before it is swallowed by the black hole irrespective of the EOS . Especially for less-compact neutron stars , the tidal disruption occurs at a more distant orbit . The tidal disruption is reflected in a cutoff frequency of the gravitational-wave spectrum , above which the spectrum amplitude exponentially decreases . A clear relation is found between the cutoff frequency of the gravitational-wave spectrum and the compactness of the neutron star . This relation also depends weakly on the stiffness of the EOS in the core region of the neutron star , suggesting that not only the compactness but also the EOS at high density is reflected in gravitational waveforms . The mass of the disk formed after the merger shows a similar correlation with the EOS , whereas the spin of the remnant black hole depends primarily on the mass ratio of the binary , and only weakly on the EOS . Properties of the remnant disks are also analyzed .