PageRank is one of popular web page ranking mechanisms, which is used by Google. It works based on link analysis. The computation of existing pagerank consumes a very significant time, i.e., in the scale of days, due to the fact that it has to find Eigen values of billion of web pages off-line. Previous attempts on reducing the computation time by shorting the time for Eigen value convergence have been carried out based on several methods, such as extrapolation, sparse linear system and quadratic extrapolation. This study proposes a new approach, i.e., using Quotient Rayleigh in the power method in order to shorten the convergence of dominant Eigen values. This modified power method resulted in a significant improvement on PageRank performance. The interpolation over n-size web pages also shows a consistent performance of the proposed approach.