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The study on $\rho-\omega$ mixing is mainly focused on vector mesons decaywith isospin I=1, namely $\rho(\omega)\to\pi^+\pi^-$ process. In this paper, wepresent the study of $\rho-\omega$ mixing in $\rho(\omega)\to\pi^+\pi^-\pi^0$(I=0) using a flavor parameterization model for $J/\psi\to VP$ process. Byfitting theoretical frame to PDG data, we obtain the SU(3)-breaking effectparameters $s_V=0.03\pm 0.12,\ s_P=0.17\pm 0.17$ and the $\rho-\omega$ mixingpolarization operator $\Pi_{\rho \omega}=0.006\pm 0.011\text{\text{GeV}}^2$.The branching ratios are also renewed when mixing effect is incorporated:$Br(J/\psi\to \omega\pi^0) = (3.64 \pm 0.37)\times 10^{-4}$, $Br(J/\psi\to\omega\eta) = (1.48 \pm 0.17)\times 10^{-3}$, $Br(J/\psi\to\omega\eta^{\prime}) = (1.55\pm 0.56)\times 10^{-4}$; they are different fromthe corresponding PDG2012 values by 19%, 15% and 15%, respectively.

$\rho - \omega$ Mixing in $J/\psi\to VP$ Decays