In its classical formulation, the well known page rank algorithm ranks web pages only based on in-links between web pages. We propose a new in-out weight based page rank algorithm. In this paper, we have introduced a new weight matrix based on both the in-links and out-links between web pages to compute the page ranks. We have illustrated the working of our algorithm using a web graph. We notice that the page rank values of the web pages computed using the original page rank algorithm and our proposed algorithm are comparable. Moreover, our algorithm is found to be efficient with respect to the time taken to compute the page rank values.