  The theta-dependent gauge theories can be studied by using holographic
duality through string theory on certain spacetimes. Via this correspondence we
consider a stack of $N_{0}$ dynamical D0-branes as D-instantons in the
background sourced by $N_{c}$ coincident non-extreme black D4-branes. According
to the gauge-gravity duality this D0-D4 brane system corresponds to Yang-Mills
theory with a theta angle at finite temperature. We solve the IIA supergravity
action by taking account into a sufficiently small backreaction of the
D-instantons and obtain an analytical solution for our D0-D4-brane
configuration. Then the dual theory in the large $N_{c}$ limit can be
holographically investigated with the gravity solution. In the dual field
theory, we find the coupling constant exhibits the property of asymptotic
freedom as it is expected in QCD. The contribution of the theta-dependence to
the free energy gets suppressed at high temperature which is basically
consistent with the calculation by using the Yang-Mills instanton. The
topological susceptibility in the large $N_{c}$ limit vanishes and this
behavior remarkably agrees with the implications from the simulation results at
finite temperature. Besides we finally find a geometrical interpretation of the
theta-dependence in this holographic system.
