Abstract：A conventional terahertz (THz) gyrotron generates radiation on a fixed frequency. This paper studies the mode jumping and frequency sweeping capability of a THz gyrotron during continuous magnetic field tuning. Theoretically speaking, since a high-order-mode cavity is usually employed, sweeping the magnetic field strength would induce radiation on a series of different modes and there is a reasonable continuous tunable bandwidth on each mode. A THz gyrotron with 2kV voltage and 2A current is potential to generate 10 independent radiation bands between 300 GHz and 500 GHz with pulse power around 0.5 kW to 1.2 kW during magnetic field tuning between 10T to 20T. It proposes a promising scheme to realize multi-band THz spectrum sweeping source for advanced high-power THz applications.