  Based on a sample of $2.25\times 10^{8} J/\psi$ events taken with the BESIII
detector at the BEPCII collider, we present the results of a study of the decay
$J/\psi\to \eta \phi\pi^{+}\pi^{-}$. The $Y(2175)$ resonance is observed in the
invariant mass spectrum of $\phi f_{0}(980)$ with a statistical significance of
greater than $10\sigma$. The corresponding mass and width are determined to be
$M=2200\pm 6 \mathrm{(stat.)} \pm 5\mathrm{(syst.)} \mathrm{MeV}/c^{2}$ and
$\Gamma=104\pm 15\mathrm{(stat.)}\pm 15\mathrm{(syst.)}$ MeV, respectively, and
the product branching fraction is measured to be $\mathcal{B}(J/\psi\to\eta
Y(2175)$, $Y(2175)\to \phi f_{0}(980)$, $f_{0}(980)\to \pi^{+}\pi^{-})=
(1.20\pm 0.14\mathrm{(stat.)}\pm 0.37 \mathrm{(syst.)})\times 10^{-4}$. The
results are consistent within errors with those of previous experiments. We
also measure the branching fraction of $J/\psi\to \phi f_1(1285)$ with
$f_1(1285)\to \eta\pi^{+}\pi^{-}$ and set upper limits on the branching
fractions for $J/\psi\to \phi\eta(1405)$/$\phi X(1835)$/$\phi X(1870)$ with
$\eta(1405)$/$X(1835)$/$X(1870)\to \eta\pi^{+}\pi^{-}$ at the 90\% confidence
level.
