  With the newly measurements of $X(3872) \to J/\psi\pi^+\pi^-$ from LHCb
Collaboration, in addition to the dominant contribution from the $\rho^0$
meson, we perform a theoretical study on the contribution of $\omega$ meson in
the $X(3872) \to J/\psi\pi^+\pi^-$ and $X(3872)\to J/\psi\pi^+\pi^-\pi^0$
processes. It is found that the recent experimental measurements on the $\pi^+
\pi^-$ invariant mass distributions can be well reproduced, and the ratio of
the couplings between $X(3872) \to J/\psi\rho^0$ and $X(3872) \to J/\psi\omega$
is also evaluated. Within the parameters extracted from the $\pi^+ \pi^-$
invariant mass distributions of the $X(3872) \to J/\psi\pi^+\pi^-$ process, the
branching fractions of the $X(3872) \to J/\psi \omega$ channel relative to that
of the $X(3872) \to J/\psi \pi^+\pi^-\pi^0$ channel and the $\pi^+ \pi^- \pi^0$
invariant mass distributions of the $X(3872) \to J/\psi \pi^+\pi^-\pi^0$ decay
are calculated, which gives a hint for the further high-statistic experiment.
