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.