In this paper, we propose an asymptotic Bayes optimal prediction algorithm for linear regression model, which reduces complexity in terms of calculation. In the field of industrial engineering, linear regression analyses are mainly applied to statistical quality control and demand forecasting, owing to effectiveness of control, prediction, analysis of structure, and so on. Recently, statistical model selection has been studied as a method of estimation for linear regression models, and applied to various problems of prediction. The statistical model selection is to select a particular model out of all candidates which include the true probabilistic model. The conventional criteria for model selection are F-value, FPE and information criteria; for example, AIC, BIC, and MDL. The mainly purposes of statistical model selection are to detect the true probability model, predict for future observations, and compress the data. Since statistical model selection has many applications, it has been studied not only in the field of statistics but also in various fields of science such as information theory, automatical control theory, and so on. In the case of estimation of the linear regression model by statistical model selection, generally, a particular model is selected by information criterion based on a previous observation from all candidates. In the linear regression analysis, the model class is a set of the combination of explanatory variables. However, in the case of prediction, it is not necessary to select a particular model. IN this case, the purpose of prediction is to acquire the accuracy estimator of the future observation. Therefore, previous studies using statistical model selection for prediction may be insufficient. On the other hand, the prediction method based on Bayes decision theory has been reported in various fields. In this method, predictions using the mixture model, which is mixing all candidates, are acquired as Bayes optimal solution, which minimizes the Bayesian mean square error. For this reason, we apply the mixture model for the linear regression models for prediction. We, at first, show that prediction by the mixture model is Bayes optimal prediction. However, it is difficult to strictly calculate the mixture probability because of the integration complexity on the parameter space. Therefore, we propose a new prediction method which removes the integration on account of reducing the complexity. Strictly speaking, we propose an asymptotic Bayes optimal prediction, which calculates the asymptotic posterior predictive distribution; i.e., mixture model. At last, we verify the effectiveness of the proposal through the simulation experiments.