In this article, the design of a fourth-harmonic gyrotron with 1-kW-level output power at 1 terahertz (THz) is presented. A unique advantage of this design is that, with a well-optimized magnetic-cusp large-orbit electron gun, the designed gyrotron can operate from first-harmonic to fourth-harmonic in multiple discrete bands by varying the confining magnetic field strength. By carefully balancing the competing modes, the gyrotron can be tuned to operate at six candidate modes, including TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2</sub> for fundamental harmonic, TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,3</sub> and TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,4</sub> for second-harmonic, TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3,5</sub> and TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3,6</sub> for third-harmonic, and TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4,8</sub> for fourth-harmonic interactions. As the main operating mode, the TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4,8</sub> can generate a peak output power of 1.68 kW, with an output efficiency of about 2.1%, and a magnetically controlled frequency tuning range of about 1.5 GHz around 1 THz. The impact of the longitudinal nonuniformity of the cavity at high-harmonic interaction was also studied. It shows that a radial tolerance of several micrometers will significantly elevate the start-oscillation current and deteriorate output performance. This design is to produce a THz source with ultra-wideband tuning capability ranging from the submillimeter-wave to 1-THz bands.