We present a study of Cu-substitution effects in 4*f*-Ce intermetallic compound CeAu_{1-}_{x}Cu_{x}Ge, with potentially unusual electronic states, in the whole concentration range (*x* = 0.0 – 1.0). The parent CeAuGe compound, crystallizing in a non-centrosymmetric hexagonal structure, is a ferromagnetic semimetal with Curie temperature 10 K. Cu-doping on Au-site of CeAuGe, CeAu_{1-}_{x}Cu_{x}Ge, changes the crystal structure from the non-centrosymmetric (*P*6_{3}*mc*) to centrosymmetric (*P*6_{3}/*mmc*) space group at the concentration *x* ∼ 0.5, where the *c*-lattice constant has a maximum value. Magnetic susceptibility and electrical resistivity measurements reveal that all Cu-doped compounds undergo magnetic phase transition near 10 K, with the maximum transition temperature of 12 K for *x* = 0.5. The neutron powder diffraction experiments show the ferromagnetic ordering of Ce^{3+} magnetic moments with a value of about 1.2 μ_{B} at 1.8 K, oriented perpendicular to the hexagonal *c*-axis. By using symmetry analysis, we have found the solutions for the magnetic structure in the ferromagnetic Shubnikov space groups *Cmc'*2_{1}*′* and *P*2_{1}*′/m'* for *x* < 0.5 and *x* ≥ 0.5, respectively. Electrical resistivity *ρ*(*T*) exhibits a metallic temperature behaviour in all compositions. The resistivity *ρ*(*T*) has a local minimum in the paramagnetic state due to Kondo effects at high doping *x* = 0.8 and 1.0. At the small Cu-doping level, *x* = 0.2, the resistivity shows a broad feature at the ferromagnetic transition temperature and an additional transition-like peculiarity at 2.5 K in the ferromagnetic state.