In the light of the deficiencies of current grid trust models based on PKI (Public Key Infrastructure), such as ambiguity certificate information and complicated identification process,a novel grid trust model based on Family Gene (FG) model was proposed. The model solves the problems existing in tradition trust models. For example, we adopt the technology of the whole sequences of information required by a user to address the ambiguity certificate information, gene identification to solve the complexity of authentication process, and gene assignment to address the complexity of visit and control. The concepts and formal definitions of grid family, family gene, gene assignment, gene identification and trust in the grid trust security domains were given. Then, the mathematical models were established. The theoretical analysis and experimental results showed that the model is a good solution to grid trust domain.