Bulk samples with nominal composition Zn0.95Co0.05O and Zn0.92Co0.05Mn0.03O were fabricated by a solid-state reaction method at 600℃. X-ray diffraction experiment showed that the peaks of secondary phase Co3O4 with a cubic structure were visible in both samples, besides the main peaks of wurtzite structure as ZnO. Magnetization measurement indicated that doping Co alone can induce ferromagnetism in ZnO itself, while the introduction of Mn significantly enhances ferromagnetism. However,both samples showed different magnetic behavior at temperatures below 50 K. It was also noted that ferromagnetic coupling interaction was weakened due to the presence of antiferromagnetic Co3O4.