We report the measurements of gamma gamma ―> eta_c(1S), eta_c(2S)―>eta' pi+ pi- with eta' decay to gamma rho and eta pi+ pi- using 941 fb-1 of data collected with the Belle detector at the KEKB asymmetric-energy e+ e- collider. First observation of eta_c(2S)―>eta' pi+ pi- with a significance 5.5 \sigma including systematic error is obtained. The products of the two-photon decay width and branching fraction of decays to eta' pi+ pi- are determined for the eta_c(1S) and eta_c(2S), respectively. A new decay mode for the eta_c(1S)―>eta' f0(2080) with f0(2080)―>pi+ pi- is observed with a statistical significance of 20 \sigma. The cross section for gamma gamma ―> eta' pi+ pi- and eta' f2(1270) are measured for the first time.