The electronic structures of spin-Peierls (SP) compound GeCuO3 have been studied by first-principles calculations with plane wave pseudo-potential method. The calculated results indicate that the 3d orbital degree of freedom for the Cu2+ has been frozen, and the unpaired electrons occupy the dx2-y2 orbits. The exchange splitting of the spin-up and spin-down dx2-y2 orbitals leads to the insulating nature of the system. GeCuO3 belongs to the category of covalent insulators, since there are very strong hybridizations between the Cu 3d and O(2) 2p states around the Fermi level. These strong covalent interactions lead to not only the deviation of the ideal spin moment of the Cu2+, but also the stabilization of the one-dimensional antiferromagnetic (AFM) ordering. We fit the spin exchange coupling constants within the Noodleman's broken symmetry methods through the calculated total energy for the various spin ordered states of GeCuO3. The calculated results indicate that the one-dimensional AFM interactions along the c axis are very strong in GeCuO3, which is the essential reason that brings on the SP transition at low temperature.