High resolution terahertz (THz) spectroscopy is available for sensitive gas detection and also useful for vibrational mode analysis of organic molecules. We developed a widely frequency tunable (0.1-7.5 THz), monochromatic coherent THz-wave Signal Generator on the basis of difference frequency generation (DFG) in a GaP crystal via excitation of phonon-polariton mode under small-angle non-collinear phase matching condition. The pump beams for DFG were supplied from semiconductor lasers as seed beams after amplification by fiber amplifiers. Then we applied it as a light source for a high resolution and high accuracy THz spectrometer. Combining with a superconducting Transition Edge Sensor (TES) bolometer cooled by a pulse tube refrigerator, a non-stop spectrometer system was realized. The system had advantages of high stability, small size, easy operation and maintenance free in the lifetime of the pump lasers. As frequency resolution and accuracy were limited by those of pump laser beams, we have newly developed a frequency control system for two beams at the same time. Frequency resolution of 8 MHz constant in whole the frequency tunable range and absolute accuracy of better than 3 MHz were evaluated by the measurements of water vapor absorptions in vacuum.