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BL Lacertae (BL Lac) was in an unprecedented bright state since 2020 August. We have conducted long-term photometric and polarimetric observations of BL Lac in optical and near-infrared (NIR) bands using the Kanata telescope in the Higashi-Hiroshima Observatory. BL Lac had simultaneously brightened in the NIR, optical, X-ray, and gamma-ray bands during the brightening period. There were two peaks of brightness in the optical and NIR bands. The degree of polarization and electric-vector position angle (EVPA) were also found to have fluctuated in the optical and NIR bands. A bluer-when-brighter trend was observed between the optical and NIR bands during the entire period of our observation. Furthermore, during the first bright period, the EVPA became parallel to the position angle of the jet. On the other hand, the polarization during the second brightening showed a different behavior from that during the first brightening. The brightenings can be explained by a combination of a shock acceleration in which a shock was generated with the perpendicular-direction shock front of the jet and a variation of the inclination angle.