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We study the charmonium $p \bar{p} \to \psi(3770) \pi^0$ reaction usingeffective lagrangian approach where the contributions from well established$N^*$ states are considered, and all parameters are fixed in the process of$e^+e^- \to p \bar{p}\pi^0$ at center of mass energy $\sqrt{s} = 3.773$ GeV.The experimental data on the line shape of the mass distribution of the $e^+e^-\to p\bar{p}\pi^0$ can be well reproduced. Based on the studying of $e^+e^- \top \bar{p}\pi^0$, the total and differential cross sections of the $p \bar{p}\to \psi(3770) \pi^0$ reaction are predicted. At the same time we evaluatedalso the cross sections of the $p \bar{p} \to \psi(3686) \pi^0$ reaction. It isshown that the contribution of nucleon pole to this reaction is largest closeto the reaction threshold. However, the interference between nucleon pole andthe other nucleon resonance can still change the angle distributionssignificantly. Those theoretical results may be test by the future experimentsat $\overline{\mbox{P}}$ANDA.

Implication the observed $\psi(3770)\to p\bar{p}\pi^0$ for studying the $p\bar{p}\to \psi(3770)\pi^0$ process