We study the band-gap structures of Lamb waves propagating in one-dimensional periodic sequences thin plate and nesting Fibonacci superlattices thin plates with different generation numbers. The dispersion curves are calculated based on the plane wave expansion method. It is found that more band gaps occur in nesting Fibonacci superlattices than in periodic phononic crystals. This is because the cells in nesting Fibonacci superlattices are quasi-periodic sequences at micro-scale, which can cause splitting of band gaps. Additionally, the periodic feature of nesting Fibonacci superlattices at macro-scale enhances Bragg scattering, which causes band gaps to become flat. As the growth of generation numbers, the characteristic of curves becomes flatter. Compared with the periodic model, the special structures of nesting Fibonacci superlattices can be used to adjust the width of band gaps and the frequency ranges of phononic crystals. (C) 2013 Elsevier B.V. All rights reserved.