A quad-band metamaterial absorber using a periodically arranged surface structure placed on an ultra-thin substrate is demonstrated in this paper. Its surface structure consists of a rectangular patch and four L-shaped structures distributed symmetrically. The surface structure is able to have strong electromagnetic interactions with incident microwaves, thereby generating four absorption peaks at different frequencies. With the aid of the near-field distributions and impedance matching analysis of the four absorption peaks, the physical mechanism of the quad-band absorption is revealed. The usage of graphene-assembled film (GAF) provides further optimization to increase the four absorption peaks and promotes the low-profile characteristic. In addition, the proposed design has good tolerance to the incident angle in vertical polarization. The proposed absorber in this paper has the potential for filtering, detection, imaging, and other communication applications.