As newly-discovered member of the MAB phases, Cr₄AlB₄ has much potential for high-temperature structural applications due to possible formation of a protective oxide scale. By use of “linear optimization procedure” and theoretical model of “bond stiffness” based on first-principle calculations, the phase stability and mechanical behavior of Cr₄AlB₄ were investigated. No imaginary frequencies in phonon dispersion indicate the intrinsic stability. The lower energy as compared with the set of other competing phases also shows the thermodynamic stability. Based on the quantificationally calculated bond stiffness by use of the model of “bond stiffness”, strong covalent bonding is present between Cr and B atoms as well as B and B atoms, while the Cr-Al (625 GPa) and B-Al (574 GPa) bond is relatively weak. It follows that Cr₄AlB₄ can be described as layered structure of strong covalently bonded Cr-B blocks interleaved by Al atomic planes where the bonding is relatively weak, similar to the well-known MAX phases, which demonstrates the similar damage tolerance and fracture toughness of Cr₄AlB₄ with the MAX phases.