This paper proposes a new framework for anomaly detection when collectively monitoring many complex systems. The prerequisite for condition-based monitoring in industrial applications is the capability of (1) capturing multiple operational states, (2) managing many similar but different assets, and (3) providing insights into the internal relationship of the variables. To meet these criteria, we propose a multi-task learning approach based on a sparse mixture of sparse Gaussian graphical models (GGMs). Unlike existing fused- and group-lasso-based approaches, each task is represented by a sparse mixture of sparse GGMs, and can handle multi-modalities. We develop a variational inference algorithm combined with a novel sparse mixture weight selection algorithm. To handle issues in the conventional automatic relevance determination (ARD) approach, we propose a new ℓ0-regularized formulation that has guaranteed sparsity in mixture weights. We show that our framework eliminates well-known issues of numerical instability in the iterative procedure of mixture model learning. We also show better performance in anomaly detection tasks on real-world data sets. To the best of our knowledge, this is the first proposal of multi-task GGM learning allowing multi-modal distributions.