To date, most of the luminous quasars known at $zsim6$ have been found to be in maximal accretion with the Eddington ratios, $lambda_{rm{Edd}}sim1$, suggesting enhanced nuclear activities in the early universe. However, this may not be the whole picture of supermassive black hole (SMBH) growth since previous studies have not reached on faint quasars that are more likely to harbor SMBHs with low $lambda_{rm{Edd}}$. To gain a better understanding on the accretion activities in quasars in the early universe, we obtained a deep near-infrared (NIR) spectrum of a quasar, IMS J220417.92+011144.8 (hereafter IMS J2204+0112), one of the faintest quasars that have been identified at $zsim6$. From the redshifted C IV $lambda 1549$ emission line in the NIR spectrum, we find that IMS J2204+0112 harbors a SMBH with about a billion solar mass and $lambda_{rm{Edd}} sim 0.1$, but with a large uncertainty in both quantities (0.41 dex). IMS J2204+0112 has one of the lowest Eddington ratios among quasars at $zsim6$, but a common value among quasars at $zsim2$. Its low $lambda_{rm{Edd}}$ can be explained with two scenarios; the SMBH growth from a stellar mass black hole through short-duration super-Eddington accretion events or from a massive black hole seed ($sim10^{5},M_{odot}$) with Eddington-limited accretion. NIR spectra of more faint quasars are needed to better understand the accretion activities of SMBHs at $z sim 6$.
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