We report the physical properties and electronic structure calculations of a layered chromium oxypnictide, Sr2Cr3As2O2, which crystallizes in a Sr2Mn3As2O2-type structure containing both CrO2 planes and Cr2As2 layers. The newly synthesized material exhibits a metallic conduction with a dominant electron-magnon scattering. Magnetic and specific-heat measurements indicate at least two intrinsic magnetic transitions below room temperature. One is an antiferromagnetic transition at 291 K, probably associated with a spin ordering in the Cr2As2 layers. Another transition is broad, occurring at around 38 K, and possibly due to a short-range spin order in the CrO2 planes. Our first-principles calculations indicate predominant two-dimensional antiferromagnetic exchange couplings, and suggest a KG-type (i.e. K2NiF4 type for CrO2 planes and G type for Cr2As2 layers) magnetic structure, with reduced moments for both Cr sublattices. The corresponding electronic states near the Fermi energy are mostly contributed from Cr-3d orbitals which weakly (modestly) hybridize with the O-2p (As-4p) orbitals in the CrO2 (Cr2As2) layers. The bare bandstructure density of states at the Fermi level is only ∼1/4 of the experimental value derived from the lowtemperature specific-heat data, consistent with the remarkable electron-magnon coupling. The title compound is argued to be a possible candidate to host superconductivity.