We study the magnetic interactions of Co doped in ZnO, with the Co atoms occupying the nearest neighbor cation sites. We perform electronic structure calculations using the local density approximation (LDA), generalized gradient approximation (GGA), and GGA+U. The Hubbard U is treated separately on d-orbitals of Zn and Co, and simultaneously on the d-orbitals of both Zn and Co. Results of GGA+U studies confirm that the nearest neighbor Co-Co pair favor antiferromagnetic interaction, where the Co spins align oppositely. This is different from the LDA and GGA predictions. A general comparison of our results with experiments shows fairly good agreement.