We studied a finite Fibonacci sequence of Co and Py stripes aligned side by side and in direct contact with each other. Calculations based on a continuous model, including exchange and dipole interactions, were performed for structures feasible for fabrication and characterization of the main properties of magnonic quasicrystals. We have shown the fractal structure of the magnonic spectrum with a number of magnonic gaps of different widths. Moreover, localization of spin waves in quasicrystals and the existence of surface spin waves in finite quaiscrystal structure is demonstrated.