We have theoretically designed and experimentally demonstrated polarization-independent all-optical switching in a nonlinear GaInAsP-InP highmesa distributed feedback (DFB) waveguide. The device, which is composed of a highmesa waveguide stripe and a vertically etched Bragg reflector, can be simply fabricated using one-step electron beam lithography and a reactive ion etching process. The device is suitable for integration with other photonic devices such as semiconductor optical amplifiers and wavelength converters. The structural birefringence of the device has a dependence on the waveguide parameters such as the refractive index and thickness of core and cladding. The structural birefringence was successfully eliminated by adjusting the width of the highmesa waveguide. The nonlinear vertical-groove DFB highmesa waveguide is attractive for a polarization-independent all-optical switch from the viewpoint of a large grating coupling coefficient, as compared with a grating-loaded DFB highmesa waveguide. The polarization dependence of the grating coupling coefficient has also been investigated experimentally. It is possible to obtain the polarization-independent grating coupling coefficient by adjusting the grating depth in the vertical-groove DFB highmesa waveguide, together with structural zero-birefringence of the device. Polarization-independent all-optical thresholding and bistable switching operations have been successfully demonstrated in the nonlinear vertical-groove DFB highmesa waveguide.