The development of new technology in the electronics industry requires new dielectric materials. It is also important to understand the charge-carrier transport mechanism in these materials. We examined the hole drift mobility in amorphous SiC dielectric thin films using the time-of-flight (TOF) method. Charge carriers were generated using an electron gun. The generated holes gave a dispersive TOF signal and the mobility was low. For electric field strengths above 4 × 105 V cm−1 the drift mobility shows a very strong dependence on the electric field and a weak temperature dependence (transport of “high-energy” charge carriers). At lower electric fields and for thermalized charge carriers the mobility is practically field independent and thermally activated. The observed phenomenon was attributed to the changes in the effective energy of the generated carriers moving in the high electric fields and consequently in the density of localized states taking part in the transport.