The concept of fractal, such as Cantor set, has been combined with the Fresnel zone plates (ZPs) to improve its imaging capability and introduce additional freedom for optimizing. In this letter, Fibonacci zone plates (FiZPs), which is generated by means of Fibonacci fractals, was proposed. The FiZPs can be constructed by the generating rules of the Fibonacci sequences similar with the Cantor set zone plate published. Numerical simulation based on Fresnel diffraction is performed to verify the on-axis intensity distribution of the FiZPs. According to the simulated results, the FiZPs can focus the incident beam as conventional zone plates as well but with fractal on-axis intensity profile. The theoretical results are also verified by the experiment by means of phase-only spatial light modulator (pSLM). Furthermore, the spiral Fibonacci zone plate (sFiZPs) was designed by overlapping the spiral phase on the FiZPs. Both numerical simulations and experiments are performed and the results are coincident well with each other.