Abstract: Admissibility of linear prediction in finite populations with arbitrary rank under quadratic loss is investigated.For the general random effects linear model,the authors obtain the necessary and sufficient conditions for a linear prediction Ｌｙｓ（Ｌｙｓ＋ａ） of  Ｑｙ to be admissible in the class of homogenous linear predictions (linear predictions) and the class that contains all predictions.

Key words: quadratic loss, random regression coefficient, finite population, linear prediction, admissibility