Polycrystalline samples of Co1−xCuxMnGe (x = 0.05, 0.10, 0.15, 0.22 and 0.35), prepared by arc melting under argon atmosphere, have been annealed at 1123 K with final furnace cooling. The samples have been investigated by powder X-ray diffraction (in function of temperature) and ac magnetic measurements (in function of temperature and applied hydrostatic pressure up to 12 kbar). On the basis of the experimental data, the (p, T ) phase diagrams have been determined. For the low Cu content (x = 0.05, 0.10 and 0.15), the compounds show a martensitic transition between the low-temperature orthorhombic crystal structure of the TiNiSi-type (space group: P nma) and the high-temperature hexagonal structure of the Ni2In-type (space group: P 63/mmc). For the high Cu content (x = 0.22 and 0.35) only the hexagonal structure is observed. All compounds undergo a transition from para-to ferromagnetic state with decreasing temperature (in case of x = 0.22 through an intermediate antiferromagnetic phase). The para-to ferromagnetic transition is fully coupled with the martensitic one for x = 0.05 at the intermediate pressure range (6 kbar ≤ p ≤ 8 kbar). Partial magnetostructural coupling is observed for x = 0.10 at ambient pressure. The Curie temperature at ambient pressure decreases from 313 K for x = 0.05 (in the orthorhombic phase) to about 250 K for the remaining compounds (in the hexagonal phase). For the Co0.85Cu0.15MnGe compound, entropy change associated with the martensitic transition has been calculated using Clausius-Clapeyron equation.