  By a suitable transformation, we present the $(n+1)$-dimensional charged
rotating solutions of Gauss-Bonnet gravity with a complete set of allowed
rotation parameters which are real in the whole spacetime. We show that these
charged rotating solutions present black hole solutions with two inner and
outer event horizons, extreme black holes or naked singularities provided the
parameters of the solutions are chosen suitable. Using the surface terms that
make the action well-defined for Gauss-Bonnet gravity and the counterterm
method for eliminating the divergences in action, we compute finite action of
the solutions. We compute the conserved and thermodynamical quantities through
the use of free energy and the counterterm method, and find that the two
methods give the same results. We also find that these quantities satisfy the
first law of thermodynamics. Finally, we perform a stability analysis by
computing the heat capacity and the determinant of Hessian matrix of mass with
respect to its thermodynamic variables in both the canonical and the
grand-canonical ensembles, and show that the system is thermally stable. This
is commensurate with the fact that there is no Hawking-Page phase transition
for black objects with zero curvature horizon.
