SiC nanofibres produced by chemical vapour reaction technique are investigated using scanning and transmission electron microscopy. The nanofibres have been found to have a crystalline core of beta-SiC sheathed with thorn-like turbostratic carbon or amorphous Si/O/C, respectively. For this material, real and imaginary part of relative permittivity is measured in a frequency range of 1 - 18 GHz at room temperature. The results reveal that the permittivity and dielectric loss in the SiC nanofibres are a magnitude higher compared with sub-microcrystalline SiC powder. Composition and nanostructure are held responsible for the difference in dielectric properties. The mechanisms of dielectric loss in the SiC nanofibres are discussed based on interfacial polarization, lattice defects in the SiC nanofibre cores and conduction loss of turbostratic carbon in the thorn-like sheath of SiC nanofibres.