The three-dimensional Co(pym)(VO₃)₂, 1, hybrid compound, where pym is pyrimidine, has been synthesized under mild hydrothermal conditions at 120 °C. The compound has been characterized by FT-IR spectroscopy, elemental analysis, thermogravimetric measurements, thermodiffractometry, UV-Vis spectroscopy, temperature-dependent magnetic susceptibility and magnetization, and finally a study of specific heat has been performed. The crystal structure of 1 was solved using single-crystal X-ray diffraction data, taking into account that the crystals of this compound are twins of two components. It crystallizes in the monoclinic system, space group C2/c, a = 12.899(5) Å, b = 9.859(2) Å, c = 7.051(1) Å, β = 111.41(3)°, Z = 4. The crystal structure is built up from edge sharing VO₅ trigonal bipyramid double chains and [CoO₄pym]_n chains. This resembles the structure of the [Co(H₂O)₂(VO₃)₂]·2H₂O compound, 2. For this reason a comparative study of their properties was carried out. Magnetic measurements of 1, performed in the 2.0 to 300 K range, reveal the existence of a weak ferromagnetic order near 3 K. This fact was confirmed with magnetization measurements, which show irreversibility characteristic of soft ferromagnets. Magnetic measurements of 2 show a 3D antiferromagnetic ordering at 2.5 K. The magnetization shows a small change of curvature indicating the occurrence of a metamagnetic transition. Specific heat measurements of both compounds confirm the 3D nature of the magnetic order. The comparative study of the magneto-structural correlations reveals that the pyrimidine molecules are responsible for the different magnetic behaviour between 1 and 2.