Computer-Generated Holograms (CGHs) can be generated by superimposing zoneplates. A zoneplate is a grating that can concentrate an incident light into a point. Since a zoneplate has a circular symmetry, we reported an algorithm that rapidly generates a zoneplate by drawing concentric circles using computer graphic techniques. However, random memory access was required in the algorithm and resulted in degradation of the computational efficiency. In this study, we propose a fast CGH generation algorithm without random memory access using run-length encoding (RLE) based recurrence relation. As a result, we succeeded in improving the calculation time by 88%, compared with that of the previous work.