In the present work, antireflective sub-wavelength structures have been fabricated on fluorescent 6H-SiC to enhance the white light extraction efficiency by using the reactive-ion etching method. Broadband and omnidirectional antireflection characteristics show that 6H-SiC with antireflective sub-wavelength structures suppress the average surface reflection significantly from 20.5 % to 1.01 % over a wide spectral range of 390-784 nm. The luminescence intensity of the fluorescent 6H-SiC could be enhanced in the whole emission angle range. It maintains an enhancement larger than 91 % up to the incident angle of 70 degrees, while the largest enhancement of 115.4 % could be obtained at 16 degrees. The antireflective sub-wavelength structures on fluorescent 6H-SiC could also preserve the luminescence spectral profile at a large emission angle by eliminating the Fabry-Pérot microcavity interference effect.