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 $V(Q)= ��^{��+4} Q^{-��}~(��\geq 2)$, we find that the density parameter of the scalar field decreases as $��_Q \sim a^{-4(��-2)/(��+2)}$ in the epoch of quadratic energy density dominance, if $��\leq 6$. 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 $��\gsim 4$.

4 pages, 2 figures