  We present a sample of 86,111 star-forming galaxies (SFGs) selected from the
catalogue of the MPA-JHU emission-line measurements for SDSS DR7 to investigate
the evolution of mass-metallicity (MZ) relation. We find that: under the $\rm
log(L_{H \alpha})>41.0$ threshold, the $0.04<z\leqslant0.06$ SFGs with $9.2<$
log($M_{\star}/M_{\sun})<9.5$ have always higher metallicities ($\sim 0.1$ dex)
than the $0.10<z<0.12$ SFGs by using the closely-matched control sample method;
under the $\rm log(L_{\OIII})>39.7$ threshold, the $0.04<z\leqslant0.06$ SFGs
with $9.2<$ log($M_{\star}/M_{\sun})<9.5$ do not exhibit the evolution of the
MZ relation, in contrast to the $0.10<z<0.12$ SFGs. We find that the
metallicity tends to be lower in galaxies with a higher concentration, higher
S\'{e}rsic index, or higher SFR. In addition, we can see that the stellar mass
and metallicity usually present higher in galaxies with a higher $D_{n}4000$ or
higher log(N/O) ratio. Moreover, we present the two galaxy populations with
log($M_{\star}/M_{\sun}$) below $10.0$ or greater than $10.5$ in the MZ
relation, showing clearly an anticorrelation and a positive correlation between
specific star formation rate and 12+log(O/H).
