A Cu(II) coordination polymer {[Cu(tmpe)_0.5(1,2-bdc)]·2CH₃CN}_n (Cu(tmpe)) (tmpe ​= ​1,1,2,2-tetra[4-(2-methyl-1H-imidazole-1-yl)phenyl]ethylene, 1,2-bdc ​= ​1,2-benzenedicarboxylate) was prepared. Cu(tmpe) has the (4,4)-connected 2D structure exhibiting the kgm topology (3²·6²·7²)₂. The series of attached g-C₃N₄ composites Cu(tmpe)/g-C₃N₄ were prepared with grinding method and the morphology, functional groups, chemical composition, thermal stability, band gap, optical properties and electrochemical performances of prepared materials were comprehensively characterized with XRD, SEM, HRTEM, EDX, FTIR, XPS, TGA, UV–Vis, PL and electrochemical tests. Cu(tmpe)/10%g-C₃N₄ had the highest catalytic efficiency for degradation of methylene blue (MB) in a series of Cu(tmpe)/wt%g-C₃N₄ (w ​= ​5, 10, 15, 20). The photocatalytic study of Cu(tmpe) and its composite Cu(tmpe)/10%g-C₃N₄ showed high efficiencies of decomposition methylene blue (MB), methyl orange (MO), methyl violet (MV), and rhodamine B (RhB) with the rates were in the order of MB ​> ​MO ​> ​MV ​> ​RhB. Cu(tmpe) and Cu(tmpe)/10%g-C₃N₄ could degrade 95.4% and 93.6% of MB after 60 ​min and 30 ​min, respectively. The photocatalytic possible mechanism of the degradation process was studied with trapping experiments as well as Mott-Schottky tests. Cu(tmpe) and Cu(tmpe)/10%g-C₃N₄ composite are good photocatalytic materials for removing organic dye pollutants from wastewater.