Trust has been recognized as an important factor for information security in open and dynamic environments, such as Internet applications, p2p systems etc. On the basis of analyzing existing trust management systems, this paper proposes a Distributed Trust Management based on Authorizing Negotiation (DTMAN). DTMAN presents a number of innovative features. First, it can authorize strangers by using authorizing negotiation, so it is very suitable for open and dynamic environments. Second, a high efficient algorithm for compliance checking is developed to support DTMAN, whose time complexity and space complexity are both O(n) (where n is the cardinality of the set of authorization credentials). The experimental result shows that the algorithm of DTMAN is more efficient than others.