We present extensively dense observations of the super-Chandrasekhar supernova (SC SN) candidate SN 2012dn from $-11$ to $+140$ days after the date of its $B$-band maximum in the optical and near-infrared (NIR) wavelengths conducted through the OISTER ToO program. The NIR light curves and color evolutions up to 35 days after the $B$-band maximum provided an excellent match with those of another SC SN 2009dc, providing a further support to the nature of SN 2012dn as a SC SN. We found that SN 2012dn exhibited strong excesses in the NIR wavelengths from $30$ days after the $B$-band maximum. The $H$ and $K_{s}$-band light curves exhibited much later maximum dates at $40$ and $70$ days after the $B$-band maximum, respectively, compared with those of normal SNe Ia. The $H$ and $K_{s}$-band light curves subtracted by those of SN 2009dc displayed plateaued evolutions, indicating a NIR echo from the surrounding dust. The distance to the inner boundary of the dust shell is limited to be $4.8 - 6.4times10^{-2}$ pc. No emission lines were found in its early phase spectrum, suggesting that the ejecta-CSM interaction could not occur. On the other hand, we found no signature that strongly supports the scenario of dust formation. The mass loss rate of the pre-explosion system is estimated to be $10^{-6}-10^{-5}$ M$_{odot}$ yr$^{-1}$, assuming that the wind velocity of the system is $10-100$ km~s$^{-1}$, which suggests that the progenitor of SN 2012dn could be a recurrent nova system. We conclude that the progenitor of this SC SN could be explained by the single-degenerate scenario.
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