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In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in thepure annihilation decay process of$\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$ induced by the $\rho$ and$\omega$ double resonance effect. Generally, the $CP$ violation is small in thepure annihilation type decay process. However, we find that the $CP$ violationcan be enhanced by double $\rho-\omega$ interference when the invariant massesof the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance. Forthe decay process of $\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$, themaximum $CP$ violation can reach 28.64{\%}.

$CP$ violation induced by the double resonance for pure annihilation decay process in Perturbative QCD