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Highlights • Graphene composite was used to prepared multilayer structure for microwave absorbing. • The multilayer absorber possesses a gradient index of characteristic impedance. • Characteristic impedance was tailored by graphene content and rod width of unit cell. • The seven-layer absorber achieved an absorption above 90% in 4.5–40 GHz. • 3D printing process was used to fabricate the complex structure. Abstract An ultra-broadband electromagnetic (EM) absorber composed of composite metamaterials was designed, fabricated and characterized. Polylactic-acid/reduced graphene oxide (PLA/RGO) composites with different amounts of RGO were prepared as a primary material collection. To provide good impedance matching and efficient wave attenuation, the multilayer absorbers were designed with a gradient index (GRIN) of characteristic impedance by manipulating the RGO content and the geometric parameters of the unit cell. The absorbers with different numbers of layers were fabricated by a material extrusion process, and then the reflection loss (RL) of the prepared samples was measured. Results showed that the methodology for designing a metamaterial absorber with gradient impedance and fabricating through a 3D printing process was effective in producing ultra-broadband absorbers. The seven-layer absorber achieved an absorption above 90% in a broad bandwidth of 4.5–40 GHz. This work could provide inspiration for upgrading the performance of some conventional absorbing composites through a rational design of the composite proportion and structure. [ABSTRACT FROM AUTHOR]