  Recent observations of quasars show high line-flux ratios in their broad
emission lines and the ratios appear to be independent of redshift up to $z
\gtrsim 6$, which indicate that the broad-line regions of these early quasars
are surprisingly metal-rich. Here, we revisit the chemical evolution of
high-redshift quasars by adding a new ingredient, i.e., the neutrino-dominated
accretion flows (NDAFs) with outflows, on top of the conventional core-collapse
supernovae (CCSNe). In the presence of the chemical contribution from NDAFs
with outflows, the total metal mass (i.e., the summation of the conventional
CCSN and NDAFs with outflows) per CCSN depends weakly upon the mass of the
progenitor star if the mass is in the range of $\sim 25-55~M_{\odot}$. We model
the chemical evolution by adopting a improved open-box model with three typical
initial mass functions (IMFs). We find that, with the additional chemical
contribution from NDAFs with outflows, the quasar metallicity can be enriched
more rapidly in the very early Universe ($z \sim 10$) and reaches higher
saturation than the no-NDAF case at $z \sim 8$, after which they evolve slowly
with redshift. The quasar metallicity can reach $\sim 20~Z_{\odot}$ ($Z_\odot$
denotes the metallicity of the Sun; and $\sim 20\%$ of which is produced by
NDAF outflows) at $z \sim 8$ for the ``top-heavy'' IMF model in
\citet{Toyouchi2022}, which readily explains the quasar observations on the
super-solar metal abundance and redshift-independent evolution.
