C/Co nanofibers (NFs) as a high-performance lightweight microwave absorber in the 2-18 GHz band were fabricated by a facile electrospinning process combined with subsequent heat treatment. The effects of Co content on the electromagnetic characteristics and microwave absorption properties of C/Co NFs were investigated. The microwave absorption performance of C/Co NFs is significantly enhanced as compared to that of pure carbon nanofibers (CNFs) and the primary microwave absorption mechanism is ascribed to the dielectric loss. With increase of Co content, the electromagnetic attenuation capability of C/Co NFs monotonically decreases, while their microwave absorbing ability firstly rises and then drops. The C/Co-5 NFs sample with 37.8wt% Co exhibits the best performance for microwave absorption due to a good impedance matching and sufficiently high electromagnetic attenuation capability, which result from proper combination and synergistic effect between Co particles and CNFs, as well as the particular Co particle@ graphite core-shell structure in the NFs. The simulation results show that a re-flection loss (RL) exceeding -20 dB is obtained in a wide frequency range of 3.2-18 GHz for the silicone composite contained only 5wt% C/Co-5 NFs by choosing an appropriate layer thickness between 1.1 mm and 5.0 mm, and an optimal RL value of -78.8 dB is obtained at a layer thickness of 2.5 mm. More importantly, when the absorber thickness is as thin as 1.5 mm, the absorption bandwidth (RL <=-20 dB) is up to about 6 GHz ranging from 12 GHz to 18 GHz, which covers the whole Ku-band. The excellent microwave absorption property together with lightweight and ultrathin thickness of C/Co NFs indicate that these magnetic carbon hybrid nanofibers can be used as a novel and promising microwave absorbing material.