A series of layered (Sr1-xKx)Fe2As2 compounds with nominal x=0-0.40 are synthesized by solid state reaction method. Similar to other parent compounds of iron-based pnictide superconductors, pure SrFe2As2 shows a strong resistivity anomaly near 210 K, which was ascribed to the spin-density-wave instability. The anomaly temperature is much higher than those observed in LaOFeAs and BaFe2As2, the two prototype parent compounds with ZrCuSiAs- and ThCr2 Si2-type structures. K-doping strongly suppresses this anomaly and induces superconductivity. Like in the case of K-doped BaFe2As2, sharp superconducting transitions at Tc～38 K is observed.We perform the Hall coefficient measurement, and confirm that the dominant carriers are hole-type. The carrier density is enhanced by a factor of 3 in comparison to F-doped LaOFeAs superconductor.