Mason et al. [8] derived theoretical results for comparing two linear forms of a common random vector by the Pitman’s closeness criterion and obtained sufficient conditions under which one of them would be superior to the other. In this paper, we compare the generalized Liu (GL) estimator to the ordinary least squares (OLS) estimator in terms of the Pitman’s closeness criterion by following the way in Mason et al. [8]. Thus, we get the comparison of the ordinary Liu estimator to the OLS estimator under the Pitman’s closeness criterion.