  Motivated by the ghost condensate model, we study the Randall-Sundrum (RS)
brane-world with an arbitrary function of the higher derivative kinetic terms,
$\mathcal{P}(X)$, where $X=-(\nabla \phi)^{2}$. The five-dimensional Einstein
equations reduce to two equations of motion with a constraint between
$\mathcal{P}(X)$ and the five-dimensional cosmological constant on the brane.
For a static extra dimension, $\mathcal{P}(X)$ has solutions for both a
negative kinetic scalar (so called {\textit{ghost}}) as well as an ordinary
scalar field. However ghost condensation cannot take place. We show that small
perturbations along the extra dimensional radius (the radion) can give rise to
ghost condensation. This produces a radiation-dominated universe and the
vanishing cosmological constant at late times but destabilizes the radion. This
instability can be resolved by an inclusion of bulk matter along $y$-direction,
which finally presents a possible explanation of the late-time cosmic
acceleration.
