  In the framework of the QCD factorization approach, we study the localized
$CP$ violations of the $B^-\rightarrow K^- \pi^+\pi^-$ decay with and without
$a_0^0(980)-f_0(980)$ mixing mechanism, respectively, and find that the
localized $CP$ violation can be enhanced by this mixing effect when the mass of
the $\pi^+\pi^-$ pair is in the vicinity of the $f_0(980)$ resonance. The
corresponding theoretical prediction results are
$\mathcal{A}_{CP}(B^-\rightarrow K f_0 \rightarrow K^-\pi^+\pi^-)=[0.24, 0.36]$
and $\mathcal{A}_{CP}(B^-\rightarrow K^- f_0(a_0) \rightarrow
K^-\pi^+\pi^-)=[0.33, 0.52]$, respectively. Meanwhile, we also calculate the
branching fraction of the $B^-\rightarrow K^-f_0(980)\rightarrow K^-\pi^+\pi^-$
decay, which is consistent with the experimental results. We suggest that
$a_0^0(980)-f_0(980)$ mixing mechanism should be considered when studying the
$CP$ violation of the $B$ or $D$ mesons decays theoretically and
experimentally.
