We propose a General Markov Framework for computing page importance. Under the framework, a Markov Skeleton Process is used to model the random walk conducted by the web surfer on a given graph. Page importance is then defined as the product of page reachability and page utility, which can be computed from the transition probability and the mean staying time of the pages in the Markov Skeleton Process respectively. We show that this general framework can cover many existing algorithms as its special cases, and that the framework can help us define new algorithms to handle more complex problems. In particular, we demonstrate the use of the framework with the exploitation of a new process named Mirror Semi-Markov Process. The experimental results validate that the Mirror Semi-Markov Process model is more effective than previous models in several tasks.