  The existence and stability analysis of an inflationary solution in a
$D+4$-dimensional anisotropic induced gravity is presented in this paper.
Nontrivial conditions in the field equations are shown to be compatible with a
cosmological model in which the 4-dimension external space evolves
inflationary, while, the D-dimension internal one is static. In particular,
only two additional constraints on the coupling constants are derived from the
abundant field equations and perturbation equations. In addition, a compact
formula for the non-redundant 4+D dimensional Friedmann equation is also
derived for convenience. Possible implications are also discussed in this
paper.
