  In the framework of Perturbative QCD (PQCD) approach we study the direct $CP$
asymmetry for the decay channel $\bar{B}_{s}\rightarrow P\pi^+\pi^-$ around the
resonance range via the $\rho-\omega$ mixing mechanism (where P refer to
pseudoscalar meson). We find that the $CP$ asymmetry can be enhanced by
$\rho-\omega$ mixing when the masses of the $\pi^+\pi^-$ pairs are at the area
of $\rho-\omega$ resonance, and the maximum $CP$ asymmetry can reach 59{\%} for
the relevant decay channels.
