Li0.35Zn0.3Fe2.35O4 and carbon nanofibers with average diameters of 160 and 360 nm, respectively, were fabricated by electrospinning technique combined with subsequent heat treatment. By dispersing the nanofibers homogeneously into a silicone rubber matrix, the relative complex permittivity and permeability of the composites containing either 60wt% Li0.35Zn0.3Fe2.35O4 nanofibers or 5wt% carbon nanofibers as fillers were measured in the frequency range of 2 similar to 18 GHz. Electromagnetic wave absorbing performance of both single-layer and double-layer microwave absorbers was evaluated according to transmission line theory. It is found that the double-layer absorbers have much better microwave absorption properties than the single-layer absorbers with the same thickness due to the proper combination of the electromagnetic characteristics resulting from the magnetic Li0.35Zn0.3Fe2.35O4 nanofibers and dielectric carbon nanofibers. When the absorbing layer is the Li0.35Zn0.3Fe2.35O4 nanofibers/silicone rubber composite with a thickness of 1.8 mm and the matching layer is the carbon nanofibers/silicone rubber composite with a thickness of 0.2 mm, the refection loss (RL) of the double-layer absorber reaches a minimum value of -47.8 dB at around 13.9 GHz and the absorption bandwidth with the RL value below -10 dB is about 8.8 GHz ranging from 9.2 similar to 18 GHz. Meanwhile, the RL value exceeding -20 dB is obtained over the range of 11.5 similar to 18 GHz, which covers the whole Ku-band. The results indicate that the optimal double-layer microwave absorbers can be a promising candidate for lightweight and highly effective microwave absorption materials in Ku-band.