Two ethylenediamine cobalt(II) oxalate complexes Co(ox)(en), 1 and $Co(ox)(en){cdot}2H_2O$, 2 have been hydrothermally synthesized and characterized by single crystal X-ray diffraction, IR spectrum, TG analysis, and magnetic measurements. In 1, Co atoms are coordinated by two bis-bidentate oxalate ions in transconfiguration to form Co(ox) chains, which are further bridged by ethylenediamine molecules to produce 2D grid layers, Co(ox)(en). In 2, Co atoms are coordinated by bridging oxalate ions in cis-configuration to form Co(ox) chains, and the additional chelation of ethylenediamine to Co atoms completes 1D zigzag chain, Co(en)(ox). Two lattice water molecules stabilize the chains through hydrogen bonding. Magnetic susceptibility measurements indicate that both complexes exhibit weak antiferromagnetic coupling between cobalt(II) ions with the susceptibility maxima at 23 K for 1 and 20 K for 2, respectively. In 1 and 2, the oxalate ligands afford a much shorter and more effective pathway for the magnetic interaction between cobalt ions compared to the ethylenediamine ligands, so the magnetic behaviors of both complexes could be well described with 1D infinite magnetic chain model.