  We investigate the evolution of the mass-metallicity (MZ) relation with a
large sample of 53,444 star-forming galaxies (SFGs) at $0.04<z<0.12$, selected
from the catalog of MPA-JHU emission-line measurements for the Sloan Digital
Sky Survey (SDSS) Data Release 7. Regarding the sample of SFGs, we correct the
observational bias and raise the aperture covering fractions to check the
reliability of the metallicity evolution. We show that (1) the redshift
evolution of log($\rm H\alpha$) and log(O III) luminosities is displayed in our
sample; (2) we find the metallicity evolution of $\sim 0.15$ dex at $\rm log
(M_*/M_\odot)\sim9.3$ in SFGs at $0.04<z<0.12$; (3) after applying the
luminosity thresholds of log$(L_{\rm H \alpha})>41.0$ and log$(L_{\rm O\
III})>39.7$, we find that metallicity evolution is shown well, and that SFR
evolution still is shown well under the latter luminosity threshold, but the
evolution is not observed under the former one; (4) the evolution of the MZ
relation seems to disappear at about $\rm log(M_{*}/M_\odot)>10.0$ after
applying the luminosity threshold of log$(L_{\rm H \alpha})>41.0$ or
log$(L_{\rm O\ III})>39.7$; (5) we find $\alpha =0.09$ and $\alpha =0.07$ in
the equation ($\mu={\rm log}M_{*}-\alpha \rm log(SFR)$) for log$(L_{\rm H
\alpha})>41.0$ and log$(L_{\rm O\ III})>39.7$ samples, respectively, and these
imply that the evolution of the MZ relation may have a weaker dependence on SFR
in our sample.
