  We propose a new quintessence scenario in the brane cosmology, assuming that
a quintessence field $Q$ is confined in our 3-dimensional brane world. With a
potential $V(Q)= \mu^{\alpha+4} Q^{-\alpha}~(\alpha\geq 2)$, we find that the
density parameter of the scalar field decreases as $\Omega_Q \sim
a^{-4(\alpha-2)/(\alpha+2)}$ in the epoch of quadratic energy density
dominance, if $\alpha\leq 6$. This attractor solution is followed by the usual
tracking quintessence scenario after a conventional Friedmann universe is
recovered. With an equipartition of initial energy density, we find a natural
and successful quintessence model for $\alpha\gsim 4$.
