Range queries for querying the current and future positions of the moving objects have received growing interests in the research community. Existing methods, however, assume that an object only moves along an anticipated path. In this paper, we study the problem of answering probabilistic range queries on moving objects based on an uncertainty model, which captures the possible movements of objects with probabilities. Evaluation of probabilistic queries is challenging due to large objects volume and costly computation. We map the uncertain movements of all objects to a dual space for indexing. By querying the index, we quickly eliminate unqualified objects and employ an approximate approach to examine the remaining candidates for final answer. We conduct a comprehensive performance study, which shows our proposal significantly reduces the number of object examinations and the overall cost of the query evaluation.