Many few-shot image classification methods focus on learning a fixed feature space from sufficient samples of seen classes that can be readily transferred to unseen classes. For different tasks, the feature space is either kept the same or only adjusted by generating attentions to query samples. However, the discriminative channels and spatial parts for comparing different query and support images in different tasks are usually different. In this paper, we propose a task-sensitive discriminative mutual attention (TDMA) network to produce task-and-sample-specific features. For each task, TDMA first generates a discriminative task embedding that encodes the inter-class separability and within-class scatter, and then employs the task embedding to enhance discriminative channels respective to this task. Given a specific query and different support images, TDMA further incorporates the task embedding and long-range dependencies to locate the discriminative parts in the spatial dimension. Experimental results on miniImageNet, tieredImageNet and FC100 datasets show the effectiveness of the proposed model.