A two-dimensional coordination polymer, [Co(mu(1,3)-SCN)(2)(mu(1,6)-dmpzdo)](n)() (where dmpzdo = 2,5-dimethylpyrazine-1,4-dioxide), has been synthesized and its crystal structure determined by X-ray crystallography. In the complex, the adjacent Co(II) ions are coordinated by mu(1,3)-SCN(-) bridging ligands which forms a one-dimensional chain along the a axis; the one-dimensional chains are further connected by mu(1,6)-dmpzdo bridging ligands which leads to the formation of a two-dimensional layer on the ac plane. The theoretical calculations reveal that a ferromagnetic coupling exists between the mu(1,3)-SCN(-) bridging Co(II) ions and an anti-ferromagnetic interaction between the mu(1,6)-dmpzdo bridging Co(II) ions, and the anti-ferromagnetic interaction is stronger than the ferromagnetic interaction. The fitting of the variable-temperature (34-300 K) magnetic susceptibilities reveals that there is an anti-ferromagnetic coupling between the bridging Co(II) ions with the magnetic coupling constant J = -3.52 cm(-1).