Cloud computing is the most popular computing model in the current information industry, and cloud is a complex system with a large number of servers and users, it has to schedule tasks frequently among the servers and manage its computing resource flexibly to meet the demand of the users. With the growing service demand and higher QoS requirement of the users, the performance of the system is facing a big challenge, and with the expanding scale of cloud computing, its energy waste problem is becoming more and more serious due to the invalid resource organization and failed task scheduling. To improve the energy efficiency of heterogeneous servers in the cloud computing system, this paper puts forward a non-cooperative game based task scheduling and computing resource allocation algorithm NG TSRA. Firstly, we use non-cooperative game to model the task scheduling and computing resource allocation process of the servers in the cloud computing system, and the server's utility function is modeled as unit power efficiency, then we prove the existence of Nash Equilibrium point of the game, and finally use a Lagrange multiplier-based distributed iteration algorithm to solve the game. The experimental results show that the proposed algorithm can improve the average power efficiency of the cloud computing system.