4-dimensional Starobinsky model, whose action has a curvature squared R^2 term, is one of the most promising inflation models. However the origin of the higher curvature term is still unknown. From the viewpoint of high energy physics, higher curvature terms should appear as a series of curvature, i.e. there must exist R^m (2<m) terms. In previous research, the authors added a R^m (2<m) term to 4-dimensional Starobinsky action and estimated the effects of the additional term on observational predictions. They got a conclusion that observational predictions are quite sensitive to the existence of R^m (2<m) term. In this talk, we extend the previous research to D-dimensional Starobinsky model, motivated by recent papers on higher dimensional Starobinsky model. This extension is reasonable because an effective action of high energy physics, which contains higher curvature terms, is expected to appear in higher dimension. First, we consider models which have R+R^n action in D dimension and clarify that ONLY D=2n model can occur successful inflation. Then we add a R^m (m is not n) term to D-dimensional Starobinsky action and estimate the effects of the additional term on observational predictions in both analytical and numerical way. In analytical approach, we got an implication that deviations of observational predictions due to the additional terms become smaller in higher dimension. In numerical approach, we could confirm this implication. Therefore we can conclude that the observational predictions of D dimensional (4<D) extended Starobinsky model are less sensitive to such terms than those of the original 4 dimensional model. This result may make easier to construct Starobinsky-like model from high energy physics.