A method of measuring continuous terahertz frequency spectrum is provided based on Whitman interference theory effect and step-scanned working mode. The continuous terahertz spectrum measurement is calculated theoretically, and the spectrum and the energy density are taken by the computer. The measuring optical structure is set up to obtain the data of terahertz frequency-spectrum and energy density distribution. The measuring data accord well with that of theoretical analysis. The silvering reflect mirror，pyroelectric detector and chopper are used to build the measuring optical path to detect the interference intensity of one point. Frequency spectrum and energy density distribution of 210 GHz continuous terahertz backward-wave oscillator (BWO) and 400 GHz Gunn oscillator are obtained by step-scanned working mode. The accuracy of this measurement is 1 GHz. These results show that, using this method the frequency spectrum and energy density distribution of continuous terahertz wave source can be measured accurately. It provides a strong support for terahertz wave imaging research.