Summary: Two-dimensional principal component analysis (2DPCA) is one of the most representative dimensionality reduction methods and the robustness degrades in the presence of noise. To improve the robustness, several 2DPCA methods using similar distance metrics were proposed to achieve the objective of the maximum projection distance or the minimum reconstruction error. However, these two objectives cannot be accomplished simultaneously or are constrained by the same projection matrix. To handle these problems, we propose a generalized robust 2DPCA method called 2DPCA-2-Lp, which joins 2-norm and \(l_p\)-norm metrics in the objective function. It aims to maximize the ratio of projected vectors to image row vectors and to fulfill the dual objectives of directly maximizing projection distances and indirectly minimizing reconstruction errors. 2DPCA-2-Lp measures the distances between row vectors of matrices rather than the distances between matrices, thus remarkably enhancing the robustness. Furthermore, the relationship between reconstruction errors and projection distances for different parameter values is analyzed theoretically under the joint-norm metric. Then, the closed greedy iterative algorithm is developed for obtaining optimal solutions. Finally, extensive experimental results on four datasets show that 2DPCA-2-Lp outperforms most existing 2DPCA methods in terms of reconstruction and classification performances and has better robustness against noise.