  The cross section of the process $e^+e^- \rightarrow \eta'J/\psi$ is measured
at center-of-mass energies from $\sqrt{s} =$ 4.178 to 4.600 GeV using data
samples corresponding to a total integrated luminosity of 11 fb$^{-1}$
collected with the BESIII detector operating at the BEPCII storage ring. The
dependence of the cross section on $\sqrt{s}$ shows an enhancement around $4.2$
GeV. While the shape of the cross section cannot be fully explained with a
single $\psi(4160)$ or $\psi(4260)$ state, a coherent sum of the two states
does provide a reasonable description of the data.
