The fractal gap-square-ring (FGSR) pattern metasurface is combined with silicon carbide fibre (SiCf) as dielectric loss layers, and the composite double-layer fractal gap-square-ring metamaterial absorber (C-DFRMA) presents broadband microwave absorption performance till the incident angle up to 45°. Reflection loss (RL) is better than -10 dB in 8.32~15.68 GHz and peak value reaches -23.36 dB. Relation of RL and permittivity spectrum of dielectric loss layers was investigated by the Debye model. The FGSR pattern metasurface has robustness to permittivity spectrum, benificial to avoiding use of magnetic loss materials. The C-DFRMA provides a new choice as broadband microwave absorber.