  Using the generalized Tsallis entropy, the Tsallis holographic dark
energy(THDE) was proposed recently. In this paper we analyze the cosmological
consequences of the THDE model with an interaction between dark energy and dark
matter $Q=H(\alpha\rho_{m}+\beta\rho_{D})$. We find that the THDE model can
explain the current accelerated cosmic expansion, and it is stable under
certain conditions. Furthermore, through investigating the dynamical analysis,
we find that there exists an attractor which represents an accelerated
expansion phase of the universe. When $\beta=0$, this attractor corresponds to
a dark energy dominated de Sitter solution and the universe can evolve into an
era which is depicted by the $\Lambda$CDM model. The age of universe in this
model is also explored.
