The high dimensional data from modern scientific discoveries introduces unique challenges to statistical modeling. Sufficient dimension reduction is a useful tool to bridge the gap through projection subspace recovery. In this talk, we present a semiparametric framework formulated on Grassmann manifolds for dimension reduction. A gradient descent estimation on Grassmann manifolds will be discussed. The proposed approach can preserve the orthogonality of the estimators, and improve the estimation efficiency over existing approaches when the features are highly correlated. Simulation studies and a real data application will be presented to demonstrate the efficacy of the proposed approach.