We constructed a GaP continuous-wave terahertz (CW-THz) signal generator based on different frequency generation that can tune automatically from 0.15 to 6.2 THz without mode-hopping. Independent frequency feedback control for the seed laser and power feedback control for the optical power amplifier realized higher accuracy and stability of the output THz-wave at the same time. After constructing THz spectrometer with the GaP CW-THz signal generator as a light source, we have confirmed frequency resolution to be 15 MHz by the measurement of the Doppler width of water vapor absorptions in vacuumed chamber, and frequency reproducibility to be within 5 MHz by comparing with absorption frequency data.