  We report a study of the $e^{+}e^{-} \to D^{+} D^{-} \pi^{+} \pi^{-}$ process
using $e^{+}e^{-}$ collision data samples with an integrated luminosity of
$2.5\,\rm{fb}^{-1}$ at center-of-mass energies from 4.36 to $4.60 \rm{GeV}$,
collected with the BESIII detector at the BEPCII storage ring. The
$D_{1}(2420)^+$ is observed in the $D^{+} \pi^{+} \pi^{-}$ mass spectrum. The
mass and width of the $D_{1}(2420)^+$ are measured to be $(2427.2\pm 1.0_{\rm
stat.}\pm 1.2_{\rm syst.}) \rm{MeV}/c^2$ and $(23.2\pm 2.3_{\rm stat.}
\pm2.3_{\rm syst.}) \rm{MeV}$, respectively. The first errors are statistical
and the second ones are systematic. In addition, the Born cross sections of the
$e^{+}e^{-} \to D_{1}(2420)^+D^- + c.c. \to D^{+} D^{-} \pi^{+} \pi^{-}$ and
$e^{+}e^{-} \to \psi(3770) \pi^{+} \pi^{-} \to D^{+} D^{-} \pi^{+} \pi^{-}$
processes are measured as a function of the center-of-mass energy.
