First-principles calculations and a tight-binding analysis predict that the iron-pnictide BaCrFeAs2 is a promising candidate for half-metallic material with fully-compensated magnetization. The transition-metal ions Cr and Fe prefer the three-dimensional intervening lattice, which yields the antiferromagnetic order of spin orientations. Due to the difference between Cr and Fe in the electronegativity, a band gap is opened at the Fermi level in the spin channel in which Fe provides the majority carriers. The selective hybridization between 3d orbitals of Cr and As:4p states due to the peculiar lattice structure of the iron-pnictide is shown to be crucial for the novel properties.