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We present our follow-up observations to search for an electromagnetic counterpart of the IceCube high-energy neutrino, IceCube-170922A. Monitoring observations of a likely counterpart, TXS 0506+056, are also described. First, we quickly took optical and near-infrared images of 7 flat-spectrum radio sources within the IceCube error region right after the neutrino detection and found a rapid flux decline of TXS 0506+056 in Kanata/HONIR J-band data. Motivated by this discovery, intensive follow-up observations of TXS 0506+056 are continuously done, including our monitoring imaging observations, spectroscopic observations, and polarimetric observations in optical and near-infrared wavelengths. TXS 0506+056 shows a large amplitude (~1.0 mag) variability in a time scale of several days or longer, although no significant variability is detected in a time scale of a day or shorter. TXS 0506+056 also shows a bluer-when-brighter trend in optical and near-infrared wavelengths. Structure functions of variabilities are examined and indicate that TXS 0506+056 is not a special blazar in terms of optical variability. Polarization measurement results of TXS 0506+056 are also discussed., Comment: 19 pages, 10 figures, 4 tables. Accepted for publication in Publications of the Astronomical Society of Japan (PASJ)