  Using a sample of $(10.09~\pm~0.04)\times10^{9} ~J/\psi$ events collected
with the BESIII detector, a partial wave analysis of
$J/\psi\to\gamma\eta^{\prime}\eta^{\prime}$ is performed. The masses and widths
of the observed resonances and their branching fractions are reported. The main
contribution is from $J/\psi\rightarrow\gamma f_0(2020)$ with
$f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}$, which is found with a
significance of greater than 25$\sigma$. The product branching fraction ${\cal
B}\left(J/\psi\rightarrow\gamma f_0(2020)\right)\cdot{\cal
B}\left(f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}\right)$ is measured to
be $(2.63\pm0.06({\rm stat.})^{+0.31}_{-0.46}({\rm syst.}))\times10^{-4}$.
