  The cross sections of $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$ at center-of-mass
energies from 3.896 to 4.600 GeV are measured using data samples collected with
the BESIII detector operating at the Beijing Electron Positron Collider. The
cross sections are found to be of the same order of magnitude as those of
$e^{+}e^{-}\to\pi^{+}\pi^{-}J/\psi$ and $e^{+}e^{-}\to\pi^{+}\pi^{-}\psi(2S)$,
but the line shape is inconsistent with the $Y$ states observed in the latter
two modes. Two structures are observed in the $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$
cross sections around 4.22 and 4.39 GeV/$c^{2}$, which we call $Y(4220)$ and
$Y(4390)$, respectively. A fit with a coherent sum of two Breit-Wigner
functions results in a mass of $(4218.4^{+5.5}_{-4.5}\pm0.9)$ MeV/$c^{2}$ and a
width of $(66.0^{+12.3}_{-8.3}\pm0.4)$ MeV for the $Y(4220)$, and a mass of
$(4391.6^{+6.3}_{-6.8}\pm1.0)$ MeV/$c^{2}$ and a width of
$(139.5^{+16.2}_{-20.6}\pm0.6)$ MeV for the $Y(4390)$, where the first
uncertainties are statistical and the second ones systematic. The statistical
significance of $Y(4220)$ and $Y(4390)$ is 10$\sigma$ over one structure
assumption.
