The complex polymer [Cu2(oxen)(pym)2]n(ClO4)2n, where oxen and pym are N,N'-(2-aminoethyl)oxamide dianion and pyrimidine, respectively, was synthesized and characterized by means of X-ray crystallography, magnetic and spectroscopic measurements. It crystallizes in the monoclinic system, space group P2(1)/c, Z = 4 with a = 8.143(2), b = 8.646(3), c = 16.787(5) angstrom and beta = 97.35(2)-degrees. The crystal structure of this compound consists of layers of a two-dimensional network arrayed along the a axis. Inside the layer, trans-oxamidato-bridged copper(II) dimers connected by pyrimidine in an asymmetric fashion spread out along the bc plane to form a 2D infinite network. The copper(II) has a square-pyramidal environment with N3O atoms forming the basal plane and a nitrogen atom from pyrimidine occupying the apical site. The magnetic study of this compound shows a strong antiferromagnetic exchange interaction with J = -582 cm-1, due to the efficiency of the oxamidato bridge in undergoing antiferromagnetic coupling between the copper(II) atoms which are separated by about 5.2 angstrom.