  We consider an improved soft-wall AdS/QCD model coupled to an
Einstein-dilaton system, which offers a way to study the deconfining and chiral
transitions simultaneously. The correlation between these two transitions has
been investigated in detail in the Einstein-dilaton-scalar system with the bulk
scalar field representing the vacuum of matters in the flavor sector of the
model. We find that the effects of the scaling dimension $\Delta$ of the dual
operator of the dilaton manifest in chiral transitions, although the equation
of state can all be matched with the two-flavor lattice results for
$\Delta=2.5, 3, 3.5$ in the decoupling case of $\beta=0$. In the weak-coupling
case with smaller $\beta$, both the equation of state and the chiral transition
exhibit a crossover behavior and turn into first-order phase transitions with
the increase of $\beta$.
