most of gear dynamic models use a constant friction coefficient or friction coefficient obtained by calculation method that contains many simplifications and assumptions. Especially when a gear has fault, previous studies lack calculation of friction coefficient. In this paper, a new method is proposed to estimate the friction coefficient of gear pairs with different pitting. Based on the strain signal of actual gear pitting damage, the proposed method combines the finite element method and optimization method to obtain the friction coefficient at the different gear pitting level. Furthermore, by using calculated friction coefficient to obtain dynamic responses of different gear pitting states, the effects in dynamic responses of different types of friction coef f icient are compared and analyzed.