Using data samples with an integrated luminosity of 4.67 fb^-1 collected by the BESIII detector operating at the BEPCII Collider, we search for the process e⁺e^- → η'ψ(2S) at center-of-mass energies from 4.66 to 4.95 GeV. No significant signal is observed, and upper limits for the Born cross sections σ^B(e⁺e^- → η'ψ(2S)) at the 90% confidence level are determined.