In this paper, a megawatt-level Ku-band gyrotron traveling-wave tube (gyro-TWT) operating in the fundamental TE01 mode is designed and simulated. To enhance the stability of high-power operation, a periodically lossy dielectric-loaded interaction structure is introduced to effectively suppress parasitic backward-wave oscillations (BWOs). Particle-in-cell (PIC) simulation results indicate that the designed gyro-TWT achieves a 3-dB bandwidth of 700 MHz. Under beam parameters of 140 kV voltage, 50 A current and input power of 50 W, the gyro-TWT achieves a stable peak output power of 1.27 MW at 14.5GHz. The corresponding beam-to-wave conversion efficiency and saturated gain are 18.17% and 44 dB, respectively.