The effect of high pressure on structural, elastic and electronic properties of CoZr intermetallic compounds has been investigated by first-principles calculations within the generalized gradient approximation (GGA). The formation energy of in-situ phases indicates that B33 CoZr is more stable than B2 CoZr under different pressures. The elastic properties of B2 and B33 CoZr, calculated via the Voigt-Reuss-Hill (VRH) approximation, increase with increasing pressure. The mechanical anisotropies are characterized by the universal anisotropy index (AU) and the Zener anisotropy index (AZ). The sound velocities, Debye temperatures and melting temperature under applied pressure are also evaluated. Furthermore, the electronic structures under high pressure show that the electronic densities of states (DOS) at the Fermi level decrease and the charge distribution changes, resulting in a decline in the structural stability for B2 and B33 CoZr compounds.