Abstract: Background: Detailed spectroscopy of neutron-rich odd-A Cu isotopes is of great importance for studying the shell evolution in the region of Ni-78. While there is experimental information on excited states in 69-73,77,79CU isotopes, the information concerning Cu-75 is very limited. Purpose: Experimentally observed single-particle, core-coupling, and proton-hole intruder states in Cu-75, will complete the systematics of these states in the chain of isotopes. Method: Excited states in Cu-75 were populated in the beta decay of Ni-75 isotopes. The Ni nuclei were produced by the in-flight fission of U-238 projectiles, and were separated, identified, and implanted in a highly segmented Si detector array for the detection of the beta-decay electrons. The beta-delayed gamma rays were detected in a HPGe cluster array. Monte Carlo shell model calculations were performed using the A3DA interaction built on the pf g(9/2)d(5/2) model space for both neutrons and protons. Results: A level scheme of Cu-75 was built up to approximate to 4 MeV by performing a gamma-gamma coincidence analysis. The excited states below 2 MeV were interpreted based on the systematics of neutron-rich odd-A Cu isotopes and the results of the shell model calculations. Conclusions: The evolution of the single-particle, core-coupling, and proton-hole intruder states in the chain of neutron-rich odd-A Cu isotopes is discussed in the present work, in connection with the newly observed level structure of Cu-75.