The demand for high-strength magnets partly limits the operating frequency of gyrotron increasing to the terahertz band, which restricts the further development of gyrotrons. To effectively solve the problems, the design of the 1- THz forth-harmonic gyrotron is proposed using a conventional 10- T superconducting magnet and is presented here. Low-temperature cooling, for example applying liquid nitrogen, is proposed to increase the limit of the Q factor and extend the effective length of the cavity. A large orbit gun is employed to reduce the mode competition problem. Applying multi-mode time-domain theory in the simulation, it was found that although the competing third-harmonic $\text{TE}_{3,6}$ mode was excited first, the fourth-harmonic TE 4,8 mode finally dominates in the steady state regime. Furthermore, the experimental scheme of the 1 THz $4^{\text{th}}$ harmonic gyrotron is demonstrated.