In many fields such as data mining, machine learning, pattern recognition and signal processing, data sets containing huge number of features are often involved. Feature selection is an essential data preprocessing technique for such high-dimensional data classification tasks. Traditional dimensionality reduction approach falls into two categories: Feature Extraction (FE) and Feature Selection (FS). Principal component analysis is an unsupervised linear FE method for projecting high-dimensional data into a low-dimensional space with minimum loss of information. It discovers the directions of maximal variances in the data. The Rough set approach to feature selection is used to discover the data dependencies and reduction in the number of attributes contained in a data set using the data alone, requiring no additional information. For selecting discriminative features from principal components, the Rough set theory can be applied jointly with PCA, which guarantees that the selected principal components will be the most adequate for classification. We call this method Rough PCA. The proposed method is successfully applied for choosing the principal features and then applying the Upper and Lower Approximations to find the reduced set of features from a gene expression data.