In this study, the structural, elastic, electronic, and bonding nature of AgZn in B2 structure under pressure have been investigated by performing first principles calculations using density functional theory. The exchange-correlation potentials were treated within the generalized gradient approximation. The calculated quantities agree well with the available results. The electronic properties, such as band structure and density of states reveal that AgZn is metallic in nature with a large overlap at the Fermi level. The single-crystal elastic stiffness constants of AgZn are investigated using the stress-strain method. Present results for elastic constants show that AgZn is mechanically stable. The chemical bonding is interpreted by calculating the density of states and electron density distribution analysis. AgZn has ionic bonding characteristic.