In this paper, we study a novel problem of influence maximization in trajectory databases that is very useful in precise location-aware advertising. It finds $k$ best trajectories to be attached with a given advertisement and maximizes the expected influence among a large group of audience. We show that the problem is NP-hard and propose both exact and approximate solutions to find the best set of trajectories. In the exact solution, we devise an expansion-based framework that enumerates trajectory combinations in a best-first manner and propose three types of upper bound estimation techniques to facilitate early termination. In addition, we propose a novel trajectory index to reduce the influence calculation cost. To support large $k$ , we propose a greedy solution with an approximation ratio of (1 − 1/e), whose performance is further optimized by a new proposed cluster-based method. We also propose a threshold method that can support any approximation ratio $\epsilon \in (0,1]$ . In addition, we extend our problem to support the scenario when there are a group of advertisements. In our experiments, we use real datasets to construct user profiles, motion patterns, and trajectory databases. The experimental results verified the efficiency of our proposed methods.