The synthesis and properties of a novel hetero-tetranuclear compound [Cr2(bpy)4(μ-O)4Nb2(C2O4)4]·3H2O (1; bpy = 2,2'-bipyridine), investigated by single-crystal X-ray diffraction, magnetization measurements, IR, UV/visible spectroscopy, electron paramagnetic resonance (EPR; X- and Q-bands and high-field), and density functional theory (DFT) calculations, are reported. Crystal structure of 1 (orthorhombic Pcab space group) consists of a square-shaped macrocyclic {Cr2(μ-O)4Nb2} core in which CrIII and NbV ions are alternately bridged by oxo ions and three uncoordinated water molecules. The intramolecular CrIII···CrIII distances through the -O-NbV-O- bridges are 7.410(2) and 7.419(2) Å, while diagonal separation is 5.406(2) Å. The temperature dependence of magnetization M(T) evidences an anti-ferromagnetic ground state, which originates from a magnetic interaction between two CrIII ions of spin 3/2 through two triatomic -O-NbV-O- diamagnetic bridges. A spin Hamiltonian appropriate for polynuclear isolated magnetic units was used. The best-fitting curve for this model is obtained with the parameters gCr = 1.992(3), J = -12.77(5) cm-1, and |D| = 0.17(4) cm-1. The CrIII···CrIII dimer model is confirmed by EPR spectra, which exhibit a pronounced change of their shape around the temperature corresponding to the intradimer coupling J. The EPR spectra simulations and DFT calculations reveal the presence of a single-ion anisotropy that is close to being uniaxial, D = -0.31 cm-1 and E = 0.024 cm-1.