To provide more trustworthy service to service requester (SR), a prior trust degree predicting method is necessary in most cases. However, in the distributed systems, trust model is so complex that it is very difficult to quantify and predict accurately. Thus, according to human psychological cognitive behavior, a trust predicting method based on back propagation neural network (BPNN) is proposed in this paper. Moreover, due to the stochastic of initial weights' assignment and search complexity for optimal weights, training algorithm can easily be trapped into local optimum, or be slow to converge or even diverge. Focusing on these problems, a learning rate in network training is proposed here. By using adaptive data mining and knowledge discovery in multidimensional trust attributes, the model also overcomes the problem of insufficient ability of data processing in traditional models.