The superposition of different optical vortices can produce composite vortex. It makes a theoretical analysis about the superposition of two planar optical vortex beams is made through the collinear superposition of two planar vort exbeams, the dist ribution of composite vortex center in dif ferent sit uations is discussed, and through the geometric analytic method the composite vortex center which is produced by two plane vortices superposed whose vortex cores are coincident is found. In the theory, the composite vortex of the circularly symmetric distribution can bg gotten through this superposition method.