In this paper, we proposed a linear discriminant approach, namely global-local Fisher discriminant analysis (GLFDA) that explicitly considers both the local and glo- bal discriminant structures embedded in data. To be spe- cific, GLFDA constructs two graphs to, respectively, model the global and local discriminant structures and then incorporates discriminant structures and local intrinsic structure, which characterizes the within-class compact- ness, into the objective function for dimensionality reduc- tion. Thus, GLFDA well encodes the discriminant information, especially the local discriminant information of data. Experimental results on AR, YALE, and UMIST databases show the effectiveness of the proposed algorithm.