Defects such as point defects, dislocations, impurities and Te precipitates always exist in Cd 1-xZnxTe ( x =0.04) crystals obtained by Bridgman and accelerated crucible rotation technique-Bridgman bulk crystal growth methods. It is important to anneal CdZnTe slices in Cd vapor to eliminate these defects. In this paper, the solid-vapor equilibrium for CdZnTe crystals is first discussed extensively based on the phase diagrams of Cd-Te and the P-T plot of Cd0.96Zn0.04Te. Through the annalysis, the annealing conditions for Cd1-xZnxTe crystals are optimized. Experimental results show that the Zn partial vapor pressure, which is higher than the equilibrium pressure within a certain range, can enhance the diffusion process of the excess Te towards the surface of the slices and thus eliminate Te precipitates. However, saturated Zn pressure causes Zn and Te concentration in surface layers of the slices far away from the stoichiometry. Intensive exchange of atoms between the slice surface and the vapor under this condition would lead to severe damage to the crystallization quality on the surface. The inter diffusion of Zn also inhibits the outer-diffusion of impurities during annealing. Thus a lower Zn partial pressure, but still lies in the solid vapor equilibrium area of the P-T plot, can help to drive out the impurities. According to the crystallization quality and the concentration distribution of slices annealed under different conditions, the annealing of CdZnTe wafers is classified into three kinds, namely de-precipitate annealing, de-impurity annealing and homogenizing annealing. The favorable annealing process should be a multi-step and multi period procedure.