As one of the high-power radiating sources in terahertz region, the output power of gyrotrons is up to several tens of kilowatts. The traditional terahertz gyrotrons are difficult to meet the needs of nuclear magnetic resonance using the dynamic nuclear polarization technique, for working in a fixed frequency. In this paper the continuous frequency tunable 0.42 THz coaxial gyrotron with 2 GHz bandwidth by mechanical tuning has been studied. The results show that the output power can keep over 8 kW level in the tuning bandwidth with unchanged operating magnetic field.