  Using a data sample of $1.31 \times 10^{9}$ $J/\psi$ events accumulated with
the BESIII detector, the decay $J/\psi\to p\bar{p}\phi$ is studied via two
decay modes, $\phi\to K^{0}_{S}K^{0}_{L}$ and $\phi\to K^{+}K^{-}$. The
branching fraction of $J/\psi\to p\bar{p}\phi$ is measured to be
$\mathcal{B}(J/\psi\to
p\bar{p}\phi)=[5.23\pm0.06(\mbox{stat})\pm0.33(\mbox{syst})]\times10^{-5}$,
which agrees well with a previously published measurement, but with a
significantly improved precision. No evident enhancement near the $p\bar{p}$
mass threshold, denoted as $X(p\bar{p})$, is observed, and the upper limit on
the branching fraction of $J/\psi\to X(p\bar{p})\phi\to p\bar{p}\phi$ is
determined to be $\mathcal{B}(J/\psi\to
  X(p\bar{p})\phi\to p\bar{p}\phi)<2.1\times10^{-7}$ at the 90\% confidence
level.
