We present a comparative study on band-gap structures of Lamb waves propagating in one-dimensional periodic sequences thin plate, Fibonacci sequences thin plate, and the nesting Fibonacci superlattices thin plates with different generation numbers respectively. By comparing among TPS in different plates, it is found that Fibonacci model doesn’t present band gaps with generation numbers , , and . Band gaps occur and split in Fibonacci model when generation number increases to . But for the nesting Fibonacci superlattices with , more band gaps occur and band gaps become very flat. With generation numbers increase to , , and , more new band gaps present. It provides flexible choices for real engineering requirement.