  Using data samples with an integrated luminosity of 22.42 fb$^{-1}$ collected
by the BESIII detector operating at the BEPCII storage ring, we measure the
cross sections of the $e^{+}e^{-}\rightarrow\etaJ/\psi$ process at
center-of-mass energies from 3.808 to 4.951 GeV. Three structures are observed
in the line shape of the measured cross sections. A maximum-likelihood fit with
$\psi(4040)$, two additional resonances, and a non-resonant component is
performed. The mass and width of the first additional state are
$(4219.7\pm2.5\pm4.5) \rm{MeV}/\rm{c}^2$ and $(80.7\pm4.4\pm1.4) \rm{MeV}$,
respectively, consistent with the $\psi(4230)$. For the second state, the mass
and width are $(4386\pm13\pm17) \rm{MeV}/\rm{c}^2$ and $(177\pm32\pm13)
\rm{MeV}$, respectively, consistent with the $\psi(4360)$. The first
uncertainties are statistical and the second ones are systematic. The
statistical significance of $\psi(4040)$ is $8.0\sigma$ and those for
$\psi(4230)$ and $\psi(4360)$ are more than $10.0\sigma$.
