The structure, anisotropic magnetic, electrical and thermal transport properties for single crystals of Ca₃Co_4−xCu_xO₉ (x = 0, 0.2, 0.4, 0.6 and 0.8) have been investigated systematically. The Cu-doping with x = 0.2 at Co-site is sufficient to drive the low-temperature spin-glass state in the Ca₃Co₄O₉ system. The value of resistivity along ab-plane decreases monotonously with increasing x in the whole temperature range studied, and around room temperature, the in-plane resistivity of Ca₃Co_3.2Cu_0.8O₉ is about 71% smaller than that of the undoped sample. The temperature region where the Fermi-liquid transport mechanism dominates becomes remarkably narrowed due to the Cu-doping while the electronic correlation in the system is enhanced. With further addition of Cu in the Ca₃Co₄O₉ system, the in-plane thermopower (S_ab) increases slowly and the room-temperature S_ab for Ca₃Co_3.2Cu_0.8O₉ is about 17% larger than that of the undoped sample. As a result, the power factor along the ab-plane is enhanced by about 3.8 times compared to the undoped sample. The results are suggested to originate from the variations of carrier concentration and electronic correlation in this system via the different Cu-doping states: Cu³⁺/Cu²⁺ (Cu³⁺ major) into the CoO₂ layer for x ≤ 0.4, while Cu²⁺/Cu³⁺ (Cu²⁺ major) into the Ca₂CoO₃ layers for x > 0.4.