This work presents an optimized damping waveguide structure designed to satisfy the radio frequency parameters and long-range transverse wakefield suppression of the 380 GeV Compact Linear Collider facility currently under study. Here, the elliptical shape of the iris and the wall shape of the damping waveguides are both optimized to reduce the magnitudes of surface electromagnetic fields. The widths of the waveguide openings of the entire sequence of damping waveguides are also decreased linearly with respect to the direction of beam propagation to strongly suppress long-range transverse wakefields and to maintain the stability of the beam. The position of the high-order-mode damping loads in the waveguide structure is also studied to make the damping waveguide structure more compact while satisfying all design targets.