  We investigate the phase structure of a charged AdS dilaton black hole in the
extended phase space which takes the cosmological constant, i.e. the
AdS-$\Lambda$ parameter as pressures. Through both thermal ensemble and
quasinormal mode analysis, we find that stable phase of the black hole with
non-trivial dilaton profiles always exists for both large and small couplings
when the AdS-$\Lambda$ is considered dynamical degrees of freedom. This forms a
somewhat contrast with previous works which does not do so. Our results provide
new examples for the parallelism or equivalences between thermal ensemble
methods and dynamic perturbation analysis for black hole phase structures.
