  We study the thermodynamic properties of black holes in dRGT massive gravity
theory using Duan's topological current $\phi-$ mapping theory. The topological
features and the corresponding thermodynamic stability conditions for neutral
and charged cases are discussed. The uncharged black hole in four dimensions
has a topological number $0$, sharing the same topological class of $D\geq6$
Gauss-Bonnet-AdS black hole. We show that the charged black hole in
four-dimensional massive gravity has the same topological structure as the
AdS-RN black hole. Further, we have extended the calculations to higher
dimensions. Our calculations strengthen the conjecture that the addition of
higher interaction terms to Einstein-Hilbert action does not alter the
topological number of black holes in four spacetime dimensions. However, in
higher dimensional massive gravity, the topological number indeed depends on
the black hole parameters.
