A new hight Tc Fe-based compound system, AFe2As2 with A = K, Cs, K/Sr and Cs/Sr has been found. Through electron-doping, Tc of the A = K and Cs compounds rises to ~37 K, and finally enter a spin-density-wave state (SDW) through further electron doping with Sr. The observation demonstrates the crucial role of the (FeAs)-layers in the superconductivity in the Fe-based layered system and the special feature of elemental A-layers in this complex chemical system may provide new avenues to superconductivity at a higher Tc.