Distributed jobs typically facing competition for multiple resources in modern data centers, especially for network. Without effective network scheduling, this competition can cause low efficiency of the data center. Previous work on network scheduling has been focused on reducing flow completion time or improving per-flow fairness. Yet, its effect on improving jobs’ performance is limited by the unawareness of relationships between communication and computation. In this paper, we focus on the problem of scheduling network resources for multiple jobs, with the specific objective to reduce the job completion time (JCT), which also makes the datacenter more efficient. With an in-depth investigation of communication and computation, we identify an opportunity for accelerating jobs in a way that occupies less bandwidth for DAG-based complicated modern jobs. Accordingly, this paper proposes JIT, a job-aware network scheduler that leverages the computational graph to accelerate jobs effectively. To cater to the goal of JIT, we first develop a mathematical model and formulate the scheduling problem as an integer linear programming (ILP) problem. We further prove that it has an equivalent linear programming (LP) problem through rigorous theoretical analysis in order to solve this ILP problem efficiently. Some reasonable simplifications are also adopted to reduce the solving time of JIT to only 1 second. The proposed JIT is simulated and compared against some state-of-the-art designs, and the simulation results demonstrate that JIT can achieve an acceleration of up to 1.55 × , which successfully improves the efficiency of the data center.