Visibility determination is one of the oldest problems in computer graphics. The visibility, in terms of back-to-front polygon visibility ordering, can be determined by updating a priority list as the viewpoint moves. A new list-priority algorithm, utilizing a property of Voronoi diagrams, is proposed in this paper. In the preprocessing phase, the 3D space is divided into Voronoi cells in order to cluster polygons that can be assigned a fixed set of priority orders within the cluster. and during the post-processing phase, the clusters and contained polygons are depth-sorted correctly. The most time-consuming work is undertaken during the pre-processing phase that only has to be executed once for the scene. All the polygons in a cluster are pre-computed to obtain the view independent priority order within the cluster. Thus, a relatively simple task is left in the post-processing phase, which is only to sort the clusters repeatedly when the viewpoint is changed. One reason to explore list-priority algorithm is because they offer flexibility that hardware configuration (such as Z-buffer approach) do not possess. One example is that of rendering with the correct treatment of the translucency effects. Translucency is an important graphics effect that can be used to increase the realism of the rendered scene or to enable more effective visual inspection in visualization.