  We construct a new class of dyonic dilaton black hole solutions in the
background of Anti-de Sitter (AdS) spacetime. In order to find an analytical
solution which satisfy all the field equations, we should consider the string
case where the dilaton coupling is $\alpha=1$. The asymptotic behaviour of the
solution ($r\rightarrow\infty$) is exactly AdS, where the dilaton field becomes
zero and the metric function reduces to $f(r)\rightarrow -\Lambda r^2/3$. In
this spacetime, black hole horizons and cosmological horizons, can be a
two-dimensional positive, zero or negative constant curvature surface. We study
the physical properties of the solution and show that depending on the metric
parameters, these solutions can describe black holes with one or two horizons
or a naked singularity. We investigate thermodynamics of the solutions by
calculating the charge, mass, temperature, entropy and the electric potential
of these solutions and disclose that these conserved and thermodynamic
quantities satisfy the first law of black hole thermodynamics. We also analyze
thermal stability of the solutions and find the conditions for which we have a
stable dyonic dilaton black hole.
