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