The technology of terahertz wave-driven dynamic nuclear-polarization-enhanced nuclear magnetic resonance (DNP-NMR) spectroscopy can improve signal sensitivity by several orders of magnitude. The terahertz gyrotron can realize a high power output and has a certain frequency-tunable range, which meets the terahertz radiation source requirements of a NMR spectroscopic system. Herein, the development of a frequency-tunable terahertz gyrotron used for the DNP-NMR spectroscopic system was introduced. The structure of a multi-section gyrotron cavity and the variation of the electron beam quality in the frequency-tunable terahertz gyrotron with the operating voltage and the operating magnetic field were also investigated. The results show that the multi-section cavity is better than the conventional three-section cavity when the terahertz frequency-tunable gyrotron used for the DNP-NMR is operating. In the design of a frequency-tunable terahertz gyrotron, not only the variation of the velocity pitch factor but also the variation of the velocity spread and the guiding center radius spread of the electron beam related to the operating voltage or the operating magnetic field should be taken into account.