  In this paper, thermodynamic properties of the Reissner-Nordstr\"om-de Sitter
(RN-dS) black hole have been studied on the basis of the correlation between
the black hole and cosmological horizons. It is found that the RN-dS black hole
experiences a phase transition, when its state parameters satisfy certain
conditions. From the analysis of the interaction between two horizons in RN-dS
spacetime, we get the numerical solution of the interaction between two
horizons. It makes us to realize the force between the black hole and
cosmological horizons, which can be regarded as a candidate to explain our
accelerating expansion universe. That provides a new window to explore the
physical mechanism of the cosmic accelerating expansion.
