Sparse two-dimensional principal component analysis (2DPCA) is an effective dimensionality reduction and data processing technique, which has been successfully applied in face recognition. Sparse 2DPCA is based on 2D image matrices instead of 1D vectors so it can well exploit the structural information of image pixels. The sparse 2DPCA model is regarded as a non-convex and non-smooth composite optimization problem. The manifold proximal gradient algorithm (ManPG) that is efficient and robust can globally converge to an optimal point in solving this kind of problem on the Stiefel manifold, such as sparse PCA. ManPG uses the proximal gradient method for the non-smooth term of this problem, which yields a convex subproblem on the tangent space. By solving this subproblem, a descent direction on the tangent space is obtained. Then a new update point on the manifold is obtained via retraction. However, in solving large-scale problems, the computational complexity of ManPG is quite high since ManPG requires calculating the full gradient in each iteration. In order to reduce the computational complexity of each iteration, a more computationally efficient Riemannian proximal stochastic gradient descent algorithm (RPSGD) is proposed, which utilizes the stochastic gradient instead of the full gradient in ManPG. We prove that the iteration complexity of the proposed RPSGD is O(1/ϵ4) while it maintains the sublinear convergence for the large-scale sparse 2DPCA. The experimental results on face recognition and handwritten digits classification data sets show RPSGD has the advantages of small-time overhead, high test accuracy, good reconstructed image quality, and relatively sparse solution in solving the large-scale sparse 2DPCA.