With the continuous enrichment of cloud services, an increasing number of applications are being deployed in data centers. These emerging applications are often communication-intensive and data-parallel, and their performance is closely related to the underlying network. With their distributed nature, the applications consist of tasks that involve a collection of parallel flows. Traditional techniques to optimize flow-level metrics are agnostic to task-level requirements, leading to poor application-level performance. In this paper, we address the heterogeneous task-level requirements of applications and propose task-aware flow scheduling. First, we model tasks’ sensitivity to their completion time by utilities. Second, on the basis of Nash bargaining theory, we establish a flow scheduling model with heterogeneous utility characteristics, and analyze it using Lagrange multiplier method and KKT condition. Third, we propose two utility-aware bandwidth allocation algorithms with different practical constraints. Finally, we present Tasch, a system that enables tasks to maintain high utilities and guarantees the fairness of utilities. To demonstrate the feasibility of our system, we conduct comprehensive evaluations with real-world traffic trace. Communication stages complete up to 1.4 $\mathrm{\times }$ faster on average, task utilities increase up to 2.26 $\mathrm{\times }$, and the fairness of tasks improves up to 8.66 $\mathrm{\times }$ using Tasch in comparison to per-flow mechanisms.