For the classes of all quadratic estimators and all quadratic estimators with their expected value independent of a fixed effect vector parameter, we propose the Bayes quadratic estimators. When one estimates unknown prior distribution from relevant data the resulting estimators are called empirical Bayes quadratic estimators (EBQE). To illustrate the development, a Monte Carlo study is carried out to compare EBQE and MVUE for three models of common practical interest. It turns out that EBQE have some advantages over MVUE, To illustrate the proposed technique we apply the new method to two real data sets