Schaffrin and Toutenburg [1] proposed a weighted mixed estimation based on the sample information and the stochastic prior information, and they also show that the weighted mixed estimator is superior to the ordinary least squares estimator under the mean squared error criterion. However, there has no paper to discuss the performance of the two estimators under the Pitman’s closeness criterion. This paper presents the comparison of the weighted mixed estimator and the ordinary least squares estimator using the Pitman’s closeness criterion. A simulation study is performed to illustrate the performance of the weighted mixed estimator and the ordinary least squares estimator under the Pitman’s closeness criterion.