Using 2917 $rm{pb}^{-1}$ of data accumulated at 3.773~$rm{GeV}$, 44.5~$rm{pb}^{-1}$ of data accumulated at 3.65~$rm{GeV}$ and data accumulated during a $psi(3770)$ line-shape scan with the BESIII detector, the reaction $e^+e^-rightarrow pbar{p}$ is studied considering a possible interference between resonant and continuum amplitudes. The cross section of $e^+e^-rightarrowpsi(3770)rightarrow pbar{p}$, $sigma(e^+e^-rightarrowpsi(3770)rightarrow pbar{p})$, is found to have two solutions, determined to be ($0.059pm0.032pm0.012$) pb with the phase angle $phi = (255.8pm37.9pm4.8)^circ$ ($<$0.11 pb at the 90% confidence level), or $sigma(e^+e^-rightarrowpsi(3770)rightarrow pbar{p}) = (2.57pm0.12pm0.12$) pb with $phi = (266.9pm6.1pm0.9)^circ$ both of which agree with a destructive interference. Using the obtained cross section of $psi(3770)rightarrow pbar{p}$, the cross section of $pbar{p}rightarrow psi(3770)$, which is useful information for the future PANDA experiment, is estimated to be either ($9.8pm5.7$) nb ($<17.2$ nb at 90% C.L.) or $(425.6pm42.9)$ nb.
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