  We revisit critical behaviour and phase structure of charged anti-deSitter
(AdS) dilaton black holes for arbitrary values of dilaton coupling $\alpha$,
and realize several novel phase behaviour for this system. We adopt the
viewpoint that cosmological constant (pressure) is fixed and treat the charge
of the black hole as a thermodynamical variable. We study critical behaviour
and phase structure by analyzing the phase diagrams in $T-S$ and $ q-T$ planes.
We numerically derive the critical point in terms of $\alpha$ and observe that
for $\alpha =1$ and $\alpha \geq \sqrt{3}$, the system does not admit any
critical point, while for $0<\alpha <1$, the critical quantities are not
significantly affected by $\alpha$. We find that unstable behavior of the Gibbs
free energy for $q<q_{c}$ exhibits a \textit{first order} (discontinuous) phase
transition between small and large black holes for $0\leq\alpha<1$. For
$1<\alpha <\sqrt{3}$ and $q>q_{c}$, however, a novel first order phase
transition occurs between small and large black hole, which has not been
observed in the previous studies on phase transition of charged AdS black
holes.
