Recent studies suggest that faint active galactic nuclei may be responsible for the reionization of the universe. Confirmation of this scenario requires spectroscopic identification of faint quasars ($M_{1450}>-24$ mag) at $z gtrsim6$, but only a very small number of such quasars have been spectroscopically identified so far. Here, we report the discovery of a faint quasar IMS J220417.92+011144.8 at z~6 in a 12.5 deg$^{2}$ region of the SA22 field of the Infrared Medium-deep Survey (IMS). The spectrum of the quasar shows a sharp break at $sim8443~rm{AA}$, with emission lines redshifted to $z=5.944 pm 0.002$ and rest-frame ultraviolet continuum magnitude $M_{1450}=-23.59pm0.10$ AB mag. The discovery of IMS J220417.92+011144.8 is consistent with the expected number of quasars at z~6 estimated from quasar luminosity functions based on previous observations of spectroscopically identified low-luminosity quasars . This suggests that the number of $M_{1450}sim-23$ mag quasars at z~6 may not be high enough to fully account for the reionization of the universe. In addition, our study demonstrates that faint quasars in the early universe can be identified effectively with a moderately wide and deep near-infrared survey such as the IMS.
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