Inspired by the idea of combining subspace learning and regularization techniques, an algorithm called locally discriminant projection of regularized least squares is proposed. To obtain projection subspace, within-class and between-class graph are constructed firstly. Then, the formula of locally discriminant projection is derived. Finally the projection subspace is worked out by regularized least squares. Compared with common algorithms, the proposed algorithm preserves the local geometrical structure of the manifold and the discriminant structure of the manifold. The experimental results on standard face database show effectiveness of the proposed algorithm.