Abstract: The structural, electronic properties, and the ferromagnetism of Co-doped orthorhombic SrZrO3 are calculated using the first-principles methods, which are performed within the density functional theory (DFT) using the projector augmented wave (PAW) implemented in the Vienna ab initio Simulation Package (VASP), and the exchange-correlation potential is treated in the local density approximation using the Ceperly-Alder scheme. SrZrO3 has been the subject of investigations because of its technological applications. For instance, the wide band gap and high dielectric constant of SrZrO3 can be used in the electronic industry, and its refractory properties are of interest in hightemperature applications.The first-principles methods have been a powerful tool for obtaining accurate ground state and indicating the relevance between the microscopic structure and the properties. The lattice parameters and atomic positions are relaxed until the total energy changed by less than 10-5 eV per conventional cell and residual force is smaller than 0.01 eV/?. All the calculations reach good convergence. The calculated results show that the Zr atoms in B sites of perovskite structure substituted by Co atoms induce the ferromagnetism in the SrZr0.875Co0.125O3. The results showed that, when the spacing between the Co-Co is 0.4097 nm, i.e. nearest neighbor, and the system is the the ferromagnetic configuration , the calculating engery is corresponding to the minimum total energy, which indicate that the Co dope into the perovskite B bit to come into being the Co ion clusters and to appear ferromagnetic. The electronic band structure diagram states clearly that the partly Zr4 + being alternated by Co become the Co4 + (3d5) to have an empty d orbital not being occupied relativing to the standardized aggregate price of Co3 + (3d6). Because of doped Co d orbitals and O p orbitals have a strong hybrid to shift up the top of the valence band and shift down the bottom of the conduction band. It means that the doped of Co reduces the band gap. It also appears the three Co3d bands(up-spin) and the seven Co3d bands(down-spin) between 0 and 2.60 eV. The substitution induces the hole due to +3 valence of Co ions. The results of the projected local densities of states shows that the doped energy level are the partly empty d orbits of the Co4+ ions. The double exchange interaction between Co3+ and Co4+ ions is believed to be the origin of magnetism in the SrZr0.875Co0.125O3 .