In this paper, the normal mixture model subjected to general linear restriction for component-means based on linear regression is proposed, and its fitting method by EM algorithm and Lagrange multiplier is provided. This model is applied to gene clustering of microarray expression data, which demonstrates it has very good performances for real data set. This model also allows to obtain the clusters that an analyst wants to find out in the fashion that the hypothesis for component-means is represented by the design matrices and the linear restriction matrices.