This theoretical investigation examines the feasibility of improving the stability of the coaxial-waveguide gyrotron traveling-wave tube (gyro-TWT) by selecting the geometrical parameter C, i.e., the ratio of the outer radius to the inner radius. The effects of the geometrical parameter C on the start-oscillation currents of oscillation modes are analyzed to determine the optimum operating conditions. Simulation results indicate that the coaxial gyro-TWT with distributed wall losses can be stably operated at a higher beam current by optimizing C. Additionally, the saturated behaviors of the operating TE01 mode are evaluated for several C values to investigate the geometrical effects on the amplification of the coaxial gyro-TWT. Moreover, performance of the fundamental harmonic coaxial gyro-TWT achieved with the optimized C value is predicted under stable operating conditions.