The superconductor Sr4V2O6Fe2As2 with transition temperature at 37.2 K was successfully fabricated. It has a layered structure with the space group of p4/nmm and with the lattice constants a=3.9296 A degrees and c=15.6732 A degrees. The observed large diamagnetization signal and zero resistance demonstrated the bulk superconductivity. The broadening of resistive transition was measured under different magnetic fields revealing a rather high upper critical field. The results also suggest a large vortex liquid region that reflects high anisotropy of the system. The Hall-effect measurements revealed dominantly electronlike charge carriers in this material. The superconductivity in the present system may be induced by oxygen deficiency or the multiple valence states of vanadium.