In a perturbative QCD approach we study the direct CP violation in the pure annihilation decay process of B¯s0→π+π-π+π- induced by the ρ and ω double resonance effect.Generally, the CP violation is small in the pure annihilation type decay process. However, we find that the CP violation can be enhanced by doubleinterference when the invariant masses of the π+π- pairs are in the vicinity of the ω resonance. For the decay process of B¯s0→π+π-π+π-, the CP violation can reach ACP(B¯s0→π+π-π+π-)=27.20-0.15-0.31-6.11+0.05+0.28+7.13%.
