A two-dimensional copper coordination polymer {[Cu2(tmipa)2(tfpt)2]·8·5H2O·CH3CN}n (Cu(tmipa)) (tmipa = tris(4-(2-methyl-1H-imidazol-1-yl)phenyl)amine, H2tfpt = 3,4,5,6-tetrafluorophthalic acid) was synthesized by solvothermal method. It has a (3,3)-connected two-dimensional structure. A series of Cu(tmipa)/wt%g-C3N4 composites (wt = 5, 10, 15, 20) were then prepared by milling, and these materials were characterized with XRD, FT-IR, SEM, TEM, EDS, XPS, TGA, UV-DRS, PL, and EIS. Cu(tmipa) degraded 92.72 % of methylene blue (MB), 91.70 % of malachite green (MG), 90.62 % of methyl orange (MO), and 92.48 % of Congo red (CR) at 50, 80, 140, and 60 min, respectively. The degradation of MB with different mass fractions of Cu(tmipa)/wt%g-C3N4 was investigated and Cu(tmipa)/15 %g-C3N4 was found to have the highest efficiency (degradation of 96.24 % of MB in 30 min). The degradation rates for Cu(tmipa)/15 %g-C3N4 were 90.88 % of MG at 60 min, 90.72 % of MO at 60 min and 96.08 % of CR. The main active species for decomposition of MB, MG, MO and CR were investigated by the active species capture experiments. The formation of heterojunction between Cu(tmipa) and g-C3N4 is the main reason for the enhancement of the decomposition efficiency, which can fully absorb the visible light and effectively avoid the recombination of electrons and holes.