In resource planning scenarios, reverse k nearest neighbor search plays an important role. However, existing reverse k nearest neighbor search on trajectories only supports spatial features of trajectories. In this paper, we introduce Reverse k Nearest Neighbors query on Semantic Trajectories (RkNNST). Given a query point from a set of geo-textual objects (e.g., POIs), the query finds those trajectories which take this query point as one of their k nearest geo-textual correlative objects. To efficiently answer RkNNST queries, we propose a novel index IMC-tree, which organizes the global and local geo-textual information on semantic-enriched trajectories. A branch-and-bound search algorithm DOTA is then designed to traverse IMC-tree with various pruning rules. To speed up the computation of correlative distance, we also design an inverted-file-based algorithm to compute without enumerating all combinations of geo-textual objects. Experiments on a real dataset validate the effectiveness and efficiency of our proposed algorithms.