The pricing mechanism of cloud-computing resources is an essential issue for both cloud customers and service providers, especially from the point of multi-provider competition. Although various mechanisms for resource provision are proposed, few studies have focused on multi-attribute resource provision with the objective of improving benefits of both cloud customers and service providers. To address the issue, we propose a price bidding mechanism for multi-attribute cloud-computing resource provision from the perspective of a non-cooperative game, in which the information of each player (customers and providers) is incomplete to others and each player wishes to maximize his/her own benefit. More specifically, considering the fairness pricing competition, we propose a novel and incentive resource provision model referring to the Quality-of-Service (QoS) and the bidding price. Then, combining with the resource provision model, the problem of price bidding is formulated as a game to find a proper price for each cloud provider. We demonstrate the existence of Nash equilibrium solution set for the formulated game model by assuming that the quantity function of provided resources from every provider is continuous. To find a Nash equilibrium solution, we propose an Equilibrium Solution Iterative (ESI) algorithm, which is proved to converge to a Nash equilibrium. Finally, a Near-equalization Price Bidding (NPB) algorithm is proposed to modify the obtained Nash equilibrium solution. Extensive simulated experiments results and the comparison experiments with the state-of-the-art and benchmark solutions validate and show the feasibility of the proposed method.