Multi-view multi-task learning has recently attracted more and more attention due to its dual-heterogeneity, i.e.,each task has heterogeneous features from multiple views, and probably correlates with other tasks via common views.Existing methods usually suffer from three problems: 1) lack the ability to eliminate noisy features, 2) hold a strict assumption on view consistency and 3) ignore the possible existence of task-view outliers.To overcome these limitations, we propose a robust method with joint group-sparsity by decomposing feature parameters into a sum of two components,in which one saves relevant features (for Problem 1) and flexible view consistency (for Problem 2),while the other detects task-view outliers (for Problem 3).With a global convergence property, we develop a fast algorithm to solve the optimization problem in a linear time complexity w.r.t. the number of features and labeled samples.Extensive experiments on various synthetic and real-world datasets demonstrate its effectiveness.