Many real-world problems exhibit the coexistence of multiple types of heterogeneity, such as view heterogeneity (i.e., multi-view property) and task heterogeneity (i.e., multi-task property). For example, in an image classification problem containing multiple poses of the same object, each pose can be considered as one view, and the detection of each type of object can be treated as one task. Furthermore, in some problems, the data type of multiple views might be different. In a web classification problem, for instance, we might be provided an image and text mixed data set, where the web pages are characterized by both images and texts. A common strategy to solve this kind of problem is to leverage the consistency of views and the relatedness of tasks to build the prediction model. In the context of deep neural network, multitask relatedness is usually realized by grouping tasks at each layer, while multi-view consistency is usually enforced by finding the maximal correlation coefficient between views. However, there is no existing deep learning algorithm that jointly models task and view dual heterogeneity, particularly for a data set with multiple modalities (text and image mixed data set or text and video mixed data set, etc.). In this paper, we bridge this gap by proposing a deep multi-task multi-view learning framework that learns a deep representation for such dual-heterogeneity problems. Empirical studies on multiple real-world data sets demonstrate the effectiveness of our proposed Deep-MTMV algorithm.