A new type of stranded carbon fiber composite core (CFCC) wire has been developed to improve the properties of the bending, torsion and resistance to lateral pressure of the carbon fiber wire. The over-sliding process of CFCC wire under the coupling actions of pulling and bending loads is the key factor to determine whether the CFCC wire is damaged or not. A CFCC wire is taken as an example to study how the bottom diameter of the pulley put impact upon the strand damage and the damage mechanism. A full-size model of CFCC wire is established with the nonlinear finite element method to study the over-sliding process. The results show that the strand damage will be improved with the increasing of the bottom diameters of the pulley, whereas the equivalent plastic strain and energy loss of the strand will decrease. It is also found that the CFCC wire damage is beyond the reasonable range when the pulley is 20 times the diameter of the CFCC wire. Moreover, it is suggested that the CFCC wire strand damage is within the allowable range when the bottom diameter of the pulley is not less than 25 times the CFCC wire diameter.