The simulation of the hole transport properties of wurtzite phase GaN are performed by the full band ensemble Monte Carlo approach. The band structure data of GaN used in the simulation are obtained by the empirical pseudopotential method. The scattering mechanisms included in the simulation are acoustic phonon scattering, optical phonon scattering, polar optical phonon scattering, piezoelectronic scattering, ionized impurity scattering, as well as the intervalley scattering. The dependence of the hole average drift velocity and average energy in three main symmetry directions for wurtzite GaN on the electric field are obtained. At room temperature, the velocity-field relation shows the non-saturated characteristics. The maximum drift velocity is about 6×106 cm s-1, and the maximum average energy is 0.12 eV in the range of the field of this work. These values are much smaller than the corresponding parameters of the electrons in GaN. Furthermore, the dependence of the diffusion mobility on the impurity density is reported.