Piece-wise smooth systems are an important class of ordinary differential equations whose dynamics are known to exhibit complex bifurcation scenarios and chaos. Broadly speaking,piece-wise smooth systems can undergo all the bifurcation that smooth ones can. More interestingly, there is a whole class of bifurcation that are unique to piece-wise smooth systems, such as the bifurcation caused by the geometric shape of the region in which the vector field is analyzed. For example (see Figure 1), the region is divided into two parts Ⅰ and Ⅱ by a discontinuity boundary which contains a corner at O. When an orbit cross the corner, border-collision bifurcation may occur (cf. [1]). The present paper deals with the mechanics of the generalized Hopf bifurcation when the stationary point locates at the corner.