Nowadays, peer-to-peer (P2P) streaming systems have become the most popular way to deliver multimedia content over the internet due to their low bandwidth requirement and high video streaming quality. However, P2P streaming systems are vulnerable to various attacks, especially pollution attacks, due to their distributed and dynamically changing infrastructure. In this paper, by exploring the unique features of various pollution attacks, we propose a trust management system tailored for P2P streaming systems. Both direct trust and indirect trust are taken into consideration in the design of the system. A new approach to model the direct trust is proposed, and a dynamic confidence factor that can dynamically adjust the weight of direct and indirect trust is also proposed. It is shown that the proposed trust management system is effective in identifying polluters and preventing them from further sharing of polluted data chunks.