We report an As-75-NMR study on iron (Fe)-based superconductors with thick perovskite-type blocking layers Sr-4(Mg0.5-xTi0.5+x)(2)O6Fe2As2 with x = 0 and 0.2. We have found that antiferromagnetic (AFM) order takes place when x = 0, and superconductivity (SC) emerges below T-c = 36 K when x = 0.2. These results reveal that the Fe-pnictides with thick perovskite-type 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 normal-state property for x = 0.2 unravels the suppression of AFM spin fluctuations at low energies, in contrast with the related Ca4Al2O6Fe2As2 with T-c = 27 K, suggesting that the AFM spin fluctuations are not a unique factor for enhancing T-c. A condition for optimizing SC should be addressed from the relation with the local tetrahedron structure of FeAs4.