Many real-world problems exhibit dual-heterogeneity. A single learning task might have features in multiple views (i.e., feature heterogeneity); multiple learning tasks might be related with each other through one or more shared views (i.e., task heterogeneity). Existing multi-task learning or multi-view learning algorithms only capture one type of heterogeneity. In this paper, we introduce Multi-Task MultiView (M2TV) learning for such complicated learning problems with both feature heterogeneity and task heterogeneity. We propose a graph-based framework (GraM2) to take full advantage of the dual-heterogeneous nature. Our framework has a natural connection to Reproducing Kernel Hilbert Space (RKHS). Furthermore, we propose an iterative algorithm (IteM2) for GraM2 framework, and analyze its optimality, convergence and time complexity. Experimental results on various real data sets demonstrate its effectiveness. Copyright 2011 by the author(s)/owner(s).