To improve the resource utilization with Quality of Service (QoS) guarantee, a task and resource scheduling method under Lyapunov optimization for container cloud queue was proposed. Firstly, based on the queueing model of cloud computing, the Lyapunov function was used to analyze the variety of the task queue length. Secondly, the minimum energy consumption objective function was constructed under the task QoS guarantee. Finally, Lyapunov optimization method was used to solve the minimum cost objective function to obtain an optimization scheduling policy for the online tasks and container resources, improving the resource utilization and guaranteeing the QoS. The CloudSim simulation results show that, the proposed task and resource scheduling policy achieves high resource utilization under the QoS guarantee, which realizes the online task and resource optimization scheduling of container cloud and provides necessary reference for cloud computing task and resource overall optimization based on queuing model.