A line-defect waveguide hosted in a 2D honeycomb photonic-crystal slab is demonstrated theoretically to realize polarization-independent waveguiding. Through an appropriate set of design parameters, a normalized bandwidth of
% subject to the condition that the common-frequency region between the transverse-electric and transverse-magnetic polarizations reaches the maximum value for a silicon-on-insulator structure. Moreover, unlike other large-bandwidth polarization-independent photonic-crystal waveguides, our structure has the highest bandwidth for a polarization-independent single-mode photonic-crystal waveguide.