We present a new technical implementation of a high-speed broadband frequency sweep of continuous-wave terahertz (THz) radiation. THz frequency sweeping with a kHz sweep rate and a THz sweep range is implemented using THz photomixing in which an optical beat source consists of a wavelength-swept laser and a distributed feedback laser diode. During the frequency sweep, frequency-domain THz interferograms are measured using the coherent homodyne detection employing signal averaging for noise reduction, which can give time-of-flight information via fast Fourier transform. Multiple reflections in a Si wafer and the thickness of the wafer are measured to demonstrate the potential of this method for fast THz tomography and thickness measurement.