Low-rank and sparsity-matrix decomposition (LRaSMD) has received considerable interests lately. One of effective methods for LRaSMD is called go decomposition (GoDec), which finds low-rank and sparse matrices iteratively subject to the predetermined low-rank matrix order <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> and sparsity cardinality <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>. This article presents an orthogonal subspace-projection (OSP) version of GoDec to be called OSP-GoDec, which implements GoDec in an iterative process by a sequence of OSPs to find desired low-rank and sparse matrices. In order to resolve the issues of empirically determining <inline-formula> <tex-math notation="LaTeX">p = m+ j </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, the well-known virtual dimensionality (VD) is used to estimate <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> in conjunction with the Kuybeda et al. developed minimax-singular value decomposition (MX-SVD) in the maximum orthogonal complement algorithm (MOCA) to estimate <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>. Consequently, LRaSMD can be realized by implementing OSP-GoDec using <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> determined by VD and MX-SVD, respectively. Its application to anomaly detection demonstrates that the proposed OSP-GoDec coupled with VD and MX-SVD performs very effectively and better than the commonly used LRaSMD-based anomaly detectors.