In the field of pattern recognition and computer vision, applying the symmetric positive definite (SPD) matrix to represent an image set is widely studied, and the remarkable performance that it yields demonstrates its effectiveness. However, the computational burden of the original SPD matrices is usually high, which may restrict the applicability of existing methods. To address this problem, we proposed an SPD manifold dimensionality reduction (DR) algorithm. Specifically, we map the original SPD manifold into a more discriminative lower-dimensional one via a learned mapping. We first construct a graph model using the mechanism of collaborative representation to characterize the local structure of the original manifold data. Then, we formulate the SPD manifold DR problem into an elaborately designed objective function introduced by the graph-embedding framework, aiming to learn the mapping. Finally, the trace optimization method is chosen to solve this optimization problem. The experimental results on some benchmark datasets demonstrate the superiority of our method over the state-of-the-art image set classification methods.