A hybrid meta-surface for achieving microwave absorption is designed based on the tunability of graphene and passive metallic structure with specific response to utilize the metallic structure and the electric properties of graphene for controlling the wave absorption. Through simulating three-dimensional full-wave electromagnetic field, the results prove the simulation to be the fact that the absorption rate at the resonant frequency can be tuned by adding the bias voltage through the square resistance of graphene, a perfect-absorption is achieved at a resistance level of 740 Ω/sq, and the absorption frequency is determined by the polypropylene thickness. The hybrid meta-surface combined with metallic structure and microwave absorber is further constructed, the metallic structure with new resonant mode is designed to increase the operation band width of the microwave absorption. The perfect absorption can achieve at 23.2 and 36.4 GHz, and the these two frequencies defines a wide band microwave absorption. The influence of structural parameters on the absorptive rate and frequency is studied. The research on tunable absorption in hybrid meta-surface is of certain scientific value in meta-surface design and graphene related applications. Key words: graphene; meta-surface; microwave absorption