In the inter-domain routing system, the running of the border gateway protocol (BGP) is on the assumption that ASes trust each other, and there is lack of effective verification on the validity of the routing information, so the false information publishers have the chance to seriously threaten the security of the inter-domain routing system. However, the existing works can not effectively limit the generation and transmission of the false routing information, so this paper presents a trust model for inter-domain routing system to achieve the trust evaluation on the routing behavior of the ASes. In this model, the evaluator’s direct evaluation of the evaluated AS’s routing behavior and the evaluated AS’s neighbors’ direct evaluation, weight value is assigned to different direct evaluation to compute the trust degree of the evaluated AS. A routing announcement behavior prediction method is used to make the direct evaluation result accurately reflect the evaluated AS’s future probability of sending true routing information. In addition, in order to promote ASes to join in the trust recommending positively, an incentive mechanism is used, in which every AS evaluates the other ASes’ recommendation behavior in history and computes the corresponding recommendation probability for them. The simulation results show that, compared with other trust models for inter-domain routing system, the trust evaluation result of our model is more accurate to reflect the evaluated AS’s future probability of sending true routing information.