A novel patch-based tessellation method for a dual subdivision scheme, the Doo-Sabin subdivision, is presented. Patch-based refinement for face-split subdivision schemes such as Catmull-Clark subdivision or Loop subdivision has been widely studied. But there is no patch-based tessellation algorithm for dual subdivision scheme [Shiue et al. 2005] yet. The method presented in this paper is the first attempt to fill up that gap. The new method uses an 1D array to hold vertices; it creates a patch corresponding to a vertex in the original mesh and does not have any numerical roundoff gaps on patch boundaries. These characteristics are different from those of patch-based refinements for face-split subdivision schemes. Experimental results show that our algorithm achieves real time tessellation performance for moderate meshes.