  We study issues of the quintessence in the brane cosmology. The initial bulk
spacetime consists of two 5D topological anti de Sitter black hole joined by
the brane (moving domain wall). Here we do not introduce any conventional
radiation and matter. Instead we include a localized scalar on the brane as a
stress-energy tensor, and thus we find the quintessence which gives an
accelerating universe. Importantly, we obtain a $\rho^2$-term as well as a
holographic matter term of $\alpha/a^4$ from the masses of the topological
black holes. We discuss a possibility that in the early universe, $\rho^2$-term
makes a large kinetic term which induces a decelerating universe. This may
provide a hint of avoiding from the perpetually accelerating universe of the
present-day quintessence. If a holographic matter term exists, it will plays
the role of a CFT-radiation in the early universe.
