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We report the magnetic properties of quasi-one-dimensional complex oxides Ca3Co2-xCuxO6 (x = 0, 0.02, 0.04, and 0.1). The rhombohedral structure (space group R[3̅]c ) peaks were well indexed in X-ray diffraction pattern. Ca3Co2O6 shows a magnetic transition at around 27 K, whereas the transition temperature for Ca3Co1.9Cu0.1O6 is around 24 K. The magnetization steps tend to disappear, revealing that they are sensitive to the Cu substitution similar to the manganese or chromium substitution systems. These results indicate that the Cu2+ ions with spin state (S = 1/2) are antiferromagnetically coupled to their Co3+ neighbors so that the ferromagnetic coupling interaction is reduced.