  Using data samples collected at center-of-mass energies between 2.000 and
3.080 GeV with the BESIII detector operating at the BEPCII collider, a
partial-wave analysis is performed on the process $e^+e^-\to\eta\pi^+\pi^-$. In
addition to the dominant $e^+e^-\to\rho\eta$ component, the $e^+e^-\to
a_2(1320)\pi$ process is also sizeable, contributing up to 24% of the total
reaction. The measured cross sections of the process $e^+e^-\to\eta\pi^+\pi^-$
are systematically higher than those of BaBar by more than $3\sigma$ at
center-of-mass energies between 2.000 and 2.300 GeV. In the cross section
lineshape for $e^+e^-\to a_2(1320)\pi$, a resonant structure is observed with a
significance of $5.5\sigma$, with $M=(2044\pm31\pm4)$ MeV/$c^2$,
$\Gamma=(163\pm69\pm24)$ MeV and
$\mathcal{B_{R}}\cdot\Gamma_{e^+e^-}^{R}=(34.6\pm17.1\pm6.0)$ eV or
$(137.1\pm73.3\pm2.1)$ eV. In the cross section lineshape for
$e^+e^-\to\rho\eta$, an evidence of a dip structure around 2180 MeV/$c^2$ is
observed with statistical significance of $3.0\sigma$.
