In high dimensionality where the number of variables are excessively larger than observations, it is required to remove the noninformative variables to cluster observations. Most model-based approaches for variable selection have been considered under the assumption of homoscedasticity and their models are mainly estimated by a penalized likelihood method. In this paper, a different approach is proposed to remove the noninformative variables effectively and to cluster based on the modified normal mixture model simultaneously. The validity of the model was provided and an EM algorithm was derived to estimate the parameters. Simulation studies and an experiment using real microarray dataset showed the effectiveness of the proposed method.