  We theoretically study a Kitaev chain with a quasiperiodic potential, where
the quasiperiodicity is introduced by a Fibonacci sequence. Based on an
analysis of the Majorana zero-energy mode, we find the critical $p$-wave
superconducting pairing potential separating a topological phase and a
non-topological phase. The topological phase diagram with respect to Fibonacci
potentials follow a self-similar fractal structure characterized by the
box-counting dimension, which is an example of the interplay of fractal and
topology like the Hofstadter's butterfly in quantum Hall insulators.
