Based on the Hill's quadratic anisotropic yield criterion, the anisotropic GTN (Gurson-Tvergaard-Needleman) mesoscopic damage model was expanded to describe the damge propogation for anisotropic voided ductile materials, which couples the plastic anisotropic behaviour and damge evolution. The isotropic GTN model based on Mises yield condition, the anisotropic GTN damage model based on Hill'48 yield criterion, and the Mises model with isotropic hardening were used to simulate a benchmark of NUMISHEET'2002, deep drawing of cylindrical cup, respectively. The damge propogation and its effect on material properties were analyzed. The result shows that the anisotropic plastic behaviour of sheet ductile material has the influence on the macroscopic mechanical properties and damge development. The void volume fraction can reflect forming histroy naturally, so it provides a theoretical foundation for prediciton of forming limit criterion under complex loading path.