Active vision is inherently attention-driven: The agent selects views of observation to best approach the vision task while improving its internal representation of the scene being observed. Inspired by the recent success of attention-based models in 2D vision tasks based on single RGB images, we propose to address the multi-view depth-based active object recognition using attention mechanism, through developing an end-to-end recurrent 3D attentional network. The architecture comprises of a recurrent neural network (RNN), storing and updating an internal representation, and two levels of spatial transformer units, guiding two-level attentions. Our model, trained with a 3D shape database, is able to iteratively attend to the best views targeting an object of interest for recognizing it, and focus on the object in each view for removing the background clutter. To realize 3D view selection, we derive a 3D spatial transformer network which is differentiable for training with back-propagation, achieving must faster convergence than the reinforcement learning employed by most existing attention-based models. Experiments show that our method outperforms state-of-the-art methods in cluttered scenes.