  Using a sample of $4.3\times 10^5$ $\eta'\to\eta\pi^0\pi^0$ events selected
from the ten billion $J/\psi$ event dataset collected with the BESIII detector,
we study the decay $\eta'\to\eta\pi^0\pi^0$ within the framework of
nonrelativistic effective field theory. Evidence for a structure at
$\pi^+\pi^-$ mass threshold is observed in the invariant mass spectrum of
$\pi^0\pi^0$ with a statistical significance of around $3.5\sigma$, which is
consistent with the cusp effect as predicted by the nonrelativistic effective
field theory. After introducing the amplitude for describing the cusp effect,
the $\pi\pi$ scattering length combination $a_0-a_2$ is determined to be $\rm
0.226\pm0.060_{stat}\pm0.013_{syst}$, which is in good agreement with
theoretical calculation of $0.2644\pm0.0051$.
