In studies to date, gait recognition across appearance changes has been a challenging task. In this paper, we present a gait recognition method that models the gait image sets as subspaces on the Grassmannian manifold. This formulation provides a convenient way to represent the subspaces as points on the manifold. By using a suitable Grassmannian kernel, the non-linear manifold can be treated as if it were a Euclidean space. This implies that conventional data analysis tool like LDA can be used on this manifold. To this end, we apply a graph based locality preserving discriminant analysis method on the Grassmannian manifold. Experiment results suggest that the proposed method can tolerate variations in appearance for gait identification.