The LIGO/Virgo detected a gravitational wave (GW) event, named GW200224_222234 (also known as S200224ca) and classified as a binary-black hole coalescence, on 2020 February 24. Given its relatively small localization skymap (71deg^2^ for a 90% credible region; revised to 50deg^2^ in GWTC-3), we performed target- of-opportunity observations using the Subaru/Hyper Suprime-Cam (HSC) in the r2 and z bands. Observations were conducted on 2020 February 25 and 28 and March 23, with the first epoch beginning 12.3hr after the GW detection. The survey covered the highest-probability sky area of 56.6deg^2^, corresponding to a 91% probability. This was the first deep follow-up (m_r_>~24, m_z_>~23) for a binary-black hole merger covering >90% of the localization. By performing image subtraction and candidate screening including light-curve fitting with transient templates and examples, we found 22 off-nucleus transients that were not ruled out as the counterparts of GW200224_222234 with our Subaru/HSC data alone. We also performed GTC/OSIRIS spectroscopy of the probable host galaxies for five candidates; two are likely to be located within the 3D skymap, whereas the others are not. In conclusion, 19 transients remain as possible optical counterparts of GW200224_222234; but we could not identify a unique promising counterpart. If there are no counterparts in the remaining candidates, the upper limits of the optical luminosity are {nu}L_{nu}_<5.2_-1.9_^+2.4^x10^41^erg/s and {nu}L_{nu}_<1.8_-0.6_^+0.8^x10^42^erg/s in the r2 and z bands, respectively, at ~12hr after GW detection. We also discuss improvements in the strategies of optical follow-ups for future GW events.