High resolution x-ray diffraction and two dimensional triple axis mapping were used to characterize a group of GaN layers of about 1.1$mu$m grown by direct current plasma molecular beam epitaxy technique on 6H-SiC(0001). A FWHM of 11.9 arcmins for an $omega$ scan and 1.2 arcmins for an $omega$/2$ heta$ scan were observed. A careful study of the rocking curves showed there were some large mosaics in the GaN layer and a tilt of $0.029^{circ}$ between the GaN layer and the SIC substrate was detected. The two dimensional triple axis mapping showed that the GaN mosaica were disoriented in the (0001) plane but rather uniformed in direction perpendicular to the plane. A mosaics were disoriented in the (0001) plane but rather uniformed in direction perpendicular to the plane. A mosaic model was deduced to explain the phenomenon and the dislocation density was estimated to be about~$10^9; extrm{cm}^{-2}$ acc ding to the model.