Measures of node ranking, such as personalized PageRank, are utilized in many web and social-network based prediction and recommendation applications. Despite their e'ectiveness when the underlying graph is certain, however, these measures become difficult to apply in the presence of uncertainties, as they are not designed for graphs that include uncertain information, such as edges that mutually exclude each other. While there are several ways to naively extend existing techniques (such as trying to encode uncertainties as edge weights or computing all possible scenarios), as we discuss in this paper, these either lead to large degrees of errors or are very expensive to compute, as the number of possible worlds can grow exponentially with the amount of uncertainty. To tackle with this challenge, in this paper, we propose an effcient Uncertain Personalized PageRank (UPPR) algorithm to approximately compute personalized PageRank values on an uncertain graph with edge uncertainties. UPPR avoids enumeration of all possible worlds, yet it is able to achieve comparable accuracy by carefully encoding edge uncertainties in a data structure that leads to fast approximations. Experimental results show that UPPR is very effcient in terms of execution time and its accuracy is comparable or beffer than more costly alternatives.