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

Partial wave analysis of $J/\psi \to \gamma \eta^{\prime} \eta^{\prime}$