We consider the theory of higher derivative gravity with non-factorizable Randall-Sundrum type space-time and obtain the metric solutions which characterize the p-brane world-volume as a curved or planar defect embedded in the higher dimensions. We consider the string inspired effective actions of the dilatonic Gauss-Bonnet type in the brane background and show its consistency with the RS brane-world scenario and the conformal weights of the dilaton couplings in the string theory with the appropriate choice of Regge slope (α′) or Gauss-Bonnet coupling (α) or both. We also discuss a time dependent dilaton solution for a string-inspired fourth-derivative gravity.