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Zone plates play an important role in X-ray and optics fileds. In this work, we proposed a generalized Fibonacci zone plates (GFiZP) is proposed, which enables the manipulation of focusing properties for X-ray and light. Compared to conventional Fibonacci zone plates (FiZPs) and Cantor-type fractal zone plates (FraZPs), this device offers additional degrees of freedom for engineering focusing performance. In comparison with FraZPs, GFiZPs are constructed with inflation rule instead of extraction rule, thus avoiding sparse structures at high recursion orders, the sparse structures would lead to issues in fabrication. Notably, numerical simulations demonstrate that, similar to FraZPs, GFiZPs retain two critical functionalities: multi-focal capability and self-similar intensity distribution. Furthermore, we conducted a detailed investigation into the axial irradiance profiles of GFiZPs with varying structural parameters. Given these favorable properties, this novel zone plate design holds great potential for expanded applications in areas such as optical manufacturing and optical manipulation of microparticles.