With increasing demands of virtual reality (VR) applications, efficient VR rendering techniques are becoming essential. Because VR stereo rendering has increased computational costs to separately render views for the left and right eyes, to reduce the rendering cost in VR applications, we present a novel traversal order for tile-based mobile GPU architectures: $Z^2$ traversal order. In tile-based mobile GPU architectures, a tile traversal order that maximizes spatial locality can increase GPU cache efficiency. For VR applications, our approach improves upon the traditional $Z$ order curve. We render corresponding screen tiles in left and right views in turn, or simultaneously, and as a result, we can exploit spatial adjacency of the two tiles. To evaluate our approach, we conducted a trace-driven hardware simulation using Mesa and a hardware simulator. Our experimental results show that $Z^2$ traversal order can reduce external memory bandwidth requirements and increase rendering performance.