New CrAs-based layered mixed-anion compounds Sr2ScCrAsO3 (SrScO-21113) and Ba3Sc2Cr2As2O5 (BaScO-32225) were synthesized, and their electronic structures and physical properties were investigated. The structures of these compounds comprise stacking of the anti-fluorite CrAs layer and perovskite-like SrScO or BaScO layers. The lattice constants of these compounds are relatively longer than those of the related compounds, such as BaCr2As2, owing to the insertion of a large perovskite blocking layer of SrScO/BaScO. While there are variations in the crystal structure of this system, such as 21113 and 32225, their chemical stability calculated by the first-principles calculations indicated that SrScO-21113 is energetically favorable compared to SrScO-32225. The formation energies of BaScO-32225 and BaScO-21113 are close to each other; in the experiment, while there was an indication of BaScO-21113 formation, only BaScO-32225 was formed as a single phase because of the low chemical stability of BaScO-21113. The partial density of states indicates that the majority of states are obtained from the 3d(4)-electrons of the Cr element hybridized modestly with p electrons at the Fermi energy. The magnetic properties of these compounds were paramagnetic, and they were different from related compounds, such as BaCr2As2, probably because of their long a-axis lengths. The temperature dependences of the electrical resistivities of both samples were in good agreement with the electronic band structure calculations. The variety of structures in the series of compounds with a CrAs layer results in different physical properties, and further development of new compounds may bring novel functionalities, such as superconductivity.