Recently, trust has been recognized as an important factor for Grid computing security. In this paper, we develop a trust management architecture for trust enhanced Grid security incorporating a novel trust model which is capable of capturing various types of trust relationships that exist in a Grid system and providing mechanisms for trust evaluation, recommendations and update for trust decisions. The outcomes of the trust decisions can then be employed by the Grid security system to formulate trust enhanced security solutions. We design several algorithms to demonstrate how one can derive the trust enhanced security solutions for both user and resource provider protection with the proposed trust management architecture. Leveraging on trust knowledge and forming it as part of the security decisions, the proposed architecture possesses several desirable emerging properties that enable it to provide an improved level of security for Grid computing systems.