Some good dimensional reduction algorithms based on image set have been developed. The core of these algorithms is performing a geometry-aware dimensionality reduction from the original manifold to a lower-dimensional, more discriminative manifold. Projection Metric Learning is a dimensional reduction algorithm that is based on Grassmann manifold. This algorithm, which is based on projection metric and RCG algorithm, has achieved better results on some benchmark datasets, but for some complicated face datasets, such as YTC, it has just obtained 66.69% classification accuracy. However, RCG algorithm has a poor performance of time efficiency. Based on the above reasons, a dimensional reduction algorithm based on the tangent space discriminant learning is presented. Firstly, perturbation is added to the projection matrix of PML to make it be a SPD matrix. Secondly LEM is adopted to map the element which lies on the SPD manifold to a tangent space, and then the iterative optimization algorithm based on eigen-decomposition is applied to find the discriminant function to obtain the transformation matrix. The experimental results on several standard datasets show the superiority of the proposed algorithm over other state-of-the-art algorithms.