In order to meet the cold testing requirements of high-frequency systems for gyrotron traveling wave tube (Gyro-TWT), a novel broadband circle waveguide TE31 mode converter is designed and verified in this letter. The designed mode converter adopts a power-divider waveguide network with twisted waveguides to realize efficient broadband conversion from TE□10 mode to TE○31 mode. Simulation results demonstrate that the proposed TE○31 mode converter exhibits an input port return loss less than -21dB and a transmission coefficient better than -0.11dB. It realizes high conversion efficiency (>97.5%) in a relative bandwidth of 41%. Prototype TE○31 mode converter is fabricated and characterized through back-to-back cold-test and infrared field pattern imaging. The experimental results closely align with the theoretical predictions.