Principal Component Analysis (PCA) is a very important Statistical analysis tool and therefore many researchers are working to improve the algorithm for better performance and better data interpretation. To improve PCA algorithm in this paper we propose to deploy a multilayer neural network with linear artificial neurons to calculate eigenvalues and corresponding eigenvectors using back-propagation learning algorithm. This approach enables us to find all the eigenvalues and its corresponding eigenvectors simultaneously by training the network. Conventional approach to calculate eigen pairs using singular value decomposition (SVD) is time consuming for large datasets because it is suitable to find one particular eigen pair during one run. The second approach that we propose for improving PCA is to decide the best eigenvectors or the principal components that best represent our original input data. This is done by extracting important features by a neural network of desired dimension from our original data by training all the features of that data.