To address the task scheduling problem in distributed systems, based on an important feature of task scheduling in distributed computing environment, we have established a non-cooperative game framework for multi-layer multi-role, and put forward a distributed reinforcement learning algorithm of the joint scheduling strategy of Nash equilibrium. Compared with static scheduling algorithm, the proposed algorithm needs less system information. It enables the scheduler to actively learn task arrival, perform related knowledge and adapt to the adjacent scheduler allocation policy. The target is to move the schedulers strategy toward Nash equilibrium. Simulation experiments show that the proposed algorithm achieves excellent performance in expected response time of tasks and fairness, compared with classical scheduling algorithms such as OLB, MET and MCT.