dimensional ( n ≥ 3) Einstein-Maxwell-dilaton gravity can be written as where R is the Ricci scalar , K (Φ) = 4( ∇ Φ) $^{2}$/ ( n − 1) is a kinetic term, V (Φ) is a potential term for the dilaton field Φ, and L (Φ , F ) = − e 4 α Φ / ( n − $^{1)}$F$_{µν}$ F µν is a coupled Lagrangian between scalar dilaton and electromagnetic fields. In L (Φ , F ), α is an arbitrary constant governing the strength of the coupling between the dilaton and the Maxwell field, F$_{µν}$ = ∂$_{µ}$A$_{ν}$ − ∂$_{ν}$A$_{µ}$ is the electromagnetic field tensor and A$_{µ}$ is the electromagnetic potential. While α = 0 corresponds to the usual Einstein-Maxwell-scalar theory, α = 1 indicates the dilaton-electromagnetic coupling that appears in the low energy string action in Einstein’s frame. Some attempts have been made to explore various solutions of Einstein-Maxwell-dilaton gravity. The dilaton field couples in a nontrivial way to other fields such as gauge fields and results into interesting solutions for the background spacetime [16, 17]. These scalar coupled black hole solutions [16, 17], however, are all asymptotically flat. It was argued that with the exception of a pure cosmological constant, no dilaton-de Sitter or anti-de Sitter black hole solution exists with the presence of only one Liouville-type dilaton potential [18]. In the presence of one or two Liouville-type potentials, black hole spacetimes which are neither asymptotically flat nor (A)dS have been explored by many authors (see e.g. [19–23]). Recently, the “cosmological constant term” in the dilaton gravity has been found by Gao and Zhang [24]. With an appropriate combination of three Liouville-type dilaton potentials, they obtained the static dilaton black hole solutions which are asymptotically (A)dS in four and higher dimensions. In such a scenario AdS spacetime constitutes the vacuum state and the black hole solution in such a spacetime becomes an important area to study [1]. For an arbitrary value of α in AdS spaces the form of the dilaton potential V (Φ) in n +1 dimensions is chosen as [24] where Λ is the cosmological constant. The motivations for studying such dilaton black holes with nonvanishing cosmological constant originate from supergravity theory. Gauged supergravity theories in various dimensions are obtained with negative cosmological constant V (Φ) = 2Λ n ( n − 2 + α $^{2}$)2 { − α 2 [ ( n + 1) 2 − ( n + 1) α 2 − 6( n + 1) + α 2 + 9 ] e − 4( n − 2)Φ / [( n − 1) α ] +( n − 2) $^{2}$( n − α $^{2}$) e 4 α Φ / ( n − 1) + 4 α $^{2}$( n − 1)( n − 2) e − 2Φ( n − 2 − α $^{2}$) / [( n − 1) α ] } , (2) 3 I = − 1 16 π ∫ d n +1 $_{x}$√ − g ( R − K (Φ) − V (Φ) + L (Φ , F )) , (1)