We report an 75As-NMR study on iron (Fe)-based superconductors with thick perovskitetype blocking layers Sr4(Mg0.5-xTi0.5+x)2O6Fe2As2 with x=0 and 0.2. We have found that antiferromagnetic (AFM) order takes place when x=0, and superconductivity (SC) emerges below Tc=36 K when x=0.2. These results reveal that the Fe-pnictides with thick perovskitetype blocks also undergo an evolution from the AFM order to the SC by doping electron carriers into FeAs planes through the chemical substitution of Ti+4 ions for Mg+2 ions, analogous to the F-substitution in LaFeAsO compound. The reason why the Tc=36 K when x=0.2 being higher than the optimally electron-doped LaFeAsO with Tc=27 K relates to the fact that the local tetrahedron structure of FeAs4 is optimized for the onset of SC.