  We present the topological solutions of Einstein-dilaton gravity in the
presence of a non-Abelian Yang-Mills field. In 4 dimensions, we consider the
$So(3)$ and $So(2,1)$ semisimple group as the Yang-Mills gauge group, and
introduce the black hole solutions with spherical and hyperbolic horizons,
respectively. The solution in the absence of dilaton potential is
asymptotically flat and exists only with spherical horizon. Contrary to the
non-extreme Reissner-Nordstrom black hole, which has two horizons with a
timelike and avoidable singularity, here the solution may present a black hole
with a null and unavoidable singularity with only one horizon. In the presence
of dilaton potential, the asymptotic behavior of the solutions is neither flat
nor anti-de Sitter. These solutions contain a null and avoidable singularity,
and may present a black hole with two horizons, an extreme black hole or a
naked singularity. We also calculate the mass of the solutions through the use
of a modified version of Brown and York formalism, and consider the first law
of thermodynamics.
