Abstract: To solve the problem of trust relationships quantitative expression and prediction in distributed open systems with a complex series of dynamic properties including uncertainty, asymmetry, part of the pass, and spatial and temporal attenuation.The eighth level trust evaluation model is built based on gray cluster theory, and the quantitative model for the trust property with evaluators and target is built based on the gray clustering coefficient matrix.The distributed trust prediction model is constructed based on dynamic gray system according to the ideas that the recent data have the greatest impact on the predicted data.The dynamic prediction of trust of on the property of target got by evaluators is achieved by using neighboring dynamic windows.The prediction is effective, and the absolute mean value of difference between the predict value and real value (0.018) is much smaller than the prediction threshold (0.05) .This trust prediction model based on social cognitive behavioral interaction results gives a new idea for trust prediction.