We propose a predictor for one step ahead observation of the statistical linear model with an error of the first-order stationary autoregressive process from the viewpoint of the generalized least squares estimation. The predictor is constructed by making use of an estimator of the autoregressive parameter based on the past observations of the process. We give an expansion up to O(1/T) for the prediction mean squared error of our predictor and show that this expansion coincides with that of the predictor with an estimator of autoregressive parameter which is independent of the past observations.