We present results from our ALMA Cycle 0 observations, at the frequencies around the HCN, HCO+, and HNC J = 4-3 transition lines, of the luminous infrared galaxy IRAS 20551-4250 at z = 0.043, which is known to host an energetically important obscured active galactic nucleus (AGN). In addition to the targeted HCN, HCO+, and HNC J = 4-3 emission lines, two additional strong emission lines are seen, which we attribute to H2S and CH3CN(+CCH). The HCN-to-HCO+ J = 4-3 flux ratio (similar to 0.7) is higher than in the other starburst-dominated galaxy (similar to 0.2) observed in our ALMA Cycle 0 program. We tentatively (similar to 5 sigma) detected the vibrationally excited (upsilon(2) = 1) HCN J = 4-3 (l = 1f) emission line, which is important for testing an infrared radiative pumping scenario for HCN. This is the second detection of this molecular transition in external galaxies. The most likely reason for this detection is not only the high flux of this emission line, but also the small molecular line widths observed in this galaxy, suggesting that vibrational excitation of HCN may be relatively common in AGN-hosting galaxies.