A novel polymeric complex of Cu(II) ion, [Cu(tfpc)2]n [tfpc: 4-(Trifluoromethyl)pyridine-2-carboxylate] has been prepared and characterized spectroscopically (by FT-IR) and structurally (by single-crystal XRD). The geometry around the Cu(II) center can be described as square planar made by tfpc ligand having nitrogen and oxygen atoms. Additionally, the Cu(II) complex has a one-dimensional double-bridged polymeric structure in which Cu(II) ions are bridged by two oxygen atoms of adjacent planes. The crystal packing has been stabilized by C[sbnd]H⋯O intra and intermolecular hydrogen bonds. The molecular structure of the Cu(II) complex has been optimized using the Density Functional Theory (DFT) B3LYP, B3PW91 and PBEPBE levels with 6-311+G(d,p) basis set. The calculated electronic spectra have been explained using the time dependent DFT (TD-DFT) method by applying the polarized continuum model (PCM). The vibrational spectral data have been calculated and compared with experimental ones. The non-linear optical (NLO) properties of the title compound have been investigated using the DFT method with three different levels. Natural Bond Orbital (NBO) property of the Cu(II) complex has been performed by the B3LYP density functional and the 6-311+G(d,p) basis set.