A copper coordination polymer with γ-aminobutyric acid (GABA), {[Cu3(GABA)2(NO3)2(OH)2(H2O)2] (NO3)2·2H2O}n (1), has been synthesized and characterized by single-crystal X-ray diffraction, IR, PXRD, TGA and elemental analysis. It exhibits a 1D chain structure including μ3-OH-Cu3 cluster as a building block. The strong H-bonding links these chains to form 2D sheet structure and the main intermolecular interaction between the 2D sheets is electrostatic interaction. According to the crystal structure of complex 1, the magnetic properties of complex 1 have been investigated by the cluster and cycle magnetic coupling models. There are three different magnetic coupling pathways of Cu(II) (J1, J2, J3) from each method and the resulting fitted curves based on the magnetic parameters of both methods compare well with the experiment values.