Herein, the crystalline structure and spin transport properties of CoCuMnSb (CCMS) half-metallic Heusler alloy have been investigated with ab-initio calculations and nonequilibrium Green's function. Experimental and theoretical results reveal that CCMS alloy stabilizes in a highly ordered LiMgPdSn-type structure with lattice parameters of a = 6.113 angstrom and alpha = 90 degrees, which match well with the reported lattice parameters of GaSb. Furthermore, the theoretical calculations indicate that CCMS exhibits perfect polarized spin at the Fermi level. Therefore, we have designed CCMS/GaSb heterostructure and CCMS/GaSb/CCMS magnetic tunnel junction (MTJ). Our architecture exhibits effective spin filtering and the MTJ produces a dramatic magnetoresistance ratio (similar to 445). These outstanding properties marks CCMS as a strong system for applications in spintronics.