A new approach to creep cavitation damage is developed by combining the basic features of continuum damage mechanics and mechanism-based cavitation models. Based on a polycrystal microstructures simulated by Voronoi tessellation, an anisotropic continuum damage variable is defined, and its evolution is given by applying the mechanism-based equations of cavity nucleation and growth to each grain boundary. Macroscopic creep deformation coupled with the damage variable is calculated by damage mechanics equations. The proposed method has been applied to investigate the damage evolution under uniaxial tension and reversed shear loading conditions.