Some peers may receive service and information of low-quality from other peers in peer-to-peer (or P2P) networks. Reputation evaluation is the normal method used to reduce the above phenomena. P2P reputation, based on score feedback, is defective because it can not distinguish the malicious feedback from the erring feedback returned by honest peers. It needs long time to converge the reputation and evaluate feedback. It is inflexible and unnatural to depict the reputation of a peer through a lot of numbers. In fact, the reputation is used to determine the rank of the peers. A reputation model called RbRf (reputation based ranking feedback) based on the rank feedback, is presented in this paper. Mathematical models unfolds in this paper show that the influence of erring feedbacks attenuates with the exponential function of RbRf. The influence of unintended malicious feedbacks is attenuated with the polynomial function in RbRf. The intended collusive feedbacks are counteracted by the correct information introduced by these feedbacks. In summary, the defection of score feedback, such as the need of a second evaluation of the trust of feedback, does not in RbRf any longer because the RbRf uses rank feedback, instead of score feedback, and the RbRf can achieve a better effect when resisting to malicious attacks. All results are verified by experimental data.