  In this paper, we investigate the topological number of de-Sitter black hole
solutions with different charges $(q)$ and rotational $(a)$ parameters. By
using generalized free energy and Duan's $\phi$-mapping topological current
theory, we find that the topological numbers of black holes can still be
classified as three types. In addition, we interestingly found the topological
classes for de-Sitter $($dS$)$ spacetime with distinct horizon, i.e, black hole
event horizon and cosmological horizon, will be different. Moreover, we also
investigate topological classifications of dS black hole solutions in higher
dimensions with or without Gauss-Bonnet term.
