  Using a low-background sample of $2.6\times 10^5$
$J/\psi\rightarrow\omega\eta(\omega\rightarrow\pi^{+}\pi^{-}\pi^{0},\eta\rightarrow\gamma\gamma)$
events, about 5 times larger statistics than previous experiments, we present a
Dalitz plot analysis of the decay $\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}$. It
is found that the Dalitz plot distribution differs from the pure $P$-wave phase
space with a statistical significance of $18.9\sigma$. The parameters from the
fit to data are in reasonable agreement with those without the cross-channel
effect within the dispersive framework, which indicates that the cross-channel
effect in $\omega\rightarrow\pi^+\pi^-\pi^0$ is not significant.
