  The $Y(4220)$ production in the process of $p\bar{p} \to Y(4220)\pi^0$ is
studied within the effective Lagrangian approach. We first study the $e^+e^-\to
Y(4220) \to p\bar{p}\pi^0$ reaction at center-of-mass energy $4.258$ GeV with
the assumption that the $Y(4220)$ is a $\psi(4S)$ state. We show that the
inclusion of nucleon and nucleon resonance leads to a quite good description of
the experimental data of $\pi^0 p$ and $\pi^0 \bar{p}$ invariant mass
distributions. Then, the total and angular distributions of the $p\bar{p} \to
Y(4220)\pi^0$ reaction are investigated. It is shown that the nucleon pole is
dominant but the contributions from excited nucleon resonances are
non-negligible. The $p\bar{p} \to Y(4220)\pi^0$ reaction is useful for studying
the property of $Y(4220)$ and our calculated results may be tested at the
forthcoming $\overline{\mbox{P}}$ANDA experiments.
