In the study of prediction filed, no matter what methods we used, the main purpose is to minimize the prediction error; however, the goals cannot be fulfilled completely. Even we choose GM (1, 1) model, which in the newest soft computing method, we also need to minimize the prediction error. In this paper, we focus on the influence parameter α in GM (1, 1) model in the first, then, analyze the characteristics of α step by step, and use numerical method to find the prediction error corresponding with α value. Second, after the mathematics model is presented, we use PSoC to design a GM (1, 1) error chip, and provides temperature prediction as our example to verify our approach.