With the rapid development of electronic and communication technology in military radar, the demand for microwave absorbing materials in low-frequency with thin layer is growing increasingly. In this study, flexible Co3O4/CC (carbon cloth) composites derives from Co-MOFs (metal-organic frameworks)/CC are prepared by hydrothermal and thermal treatment processes. The flexible precursors of Co-MOFs/CC are calcined with different calcination temperatures, which the material structure, dielectric properties and microwave absorption performance are changed. With the increase of calcination temperature, the minimum reflection loss of the corresponding Co3O4/CC composites gradually moves to the lower frequency with thinner thickness. In addition, the Co3O4/CC composites with 25 wt% filler loading ratio exhibit the minimum reflection loss (RL) of -46.59 dB at 6.24 GHz with 4.2 mm thickness. When the thickness is 3.70 mm, the effective absorption bandwidth is 3.04 GHz from 5.84 to 8.88 GHz. This study not only proves that the composite Co3O4/CC is a kind of outstanding microwave absorbing material with better flexibility, but also provides a useful inspiration for the low frequency and broadband microwave absorbing material.