We report a terahertz time-domain spectrometer with more than 6 THz spectral coverage and 1 GHz resolution based on high-speed asynchronous optical sampling. It operates at 2 kHz scan rate without mechanical delay stage. The frequency error of the system at 60 s acquisition time is determined by comparing a measured water vapor absorption spectrum to data reported in the HITRAN database. The mean error of 87 evaluated absorption lines is 142 MHz. (C) 2009 Optical Society of America