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An important challenge regarding peer's trust valuation in peer-to-peer (P2P) networks is how to cope with such problems as dishonest feedbacks of malicious peers and collusions, which cannot be effectively tackled by the existing solutions. So a recommendation belief (RB)-based distributed trust management model for P2P networks, named RBTrust for short, is proposed to quantify and evaluate the trustworthiness of peers. In RBTrust, the factor of RB is introduced to be used as the confidence metric for depicting the extent to which the recommendation peer trusts its recommendations, which is related to three aspects, including the density of interaction experiences with the trustee, the altering scope of interaction experiences and the interacting time. Besides, we consider the recommendation credibility (RC), which is constructed with the similarity function to describe the veracity of its recommendations, and time fading characteristics of trust. Theoretical analyses and experimental results demonstrate that RBTrust has advantages in combating some malicious activities such as the dishonest recommendation from malicious peers, collusions over the existing models, and show more adaptivity and effectiveness.