Trajectory search has long been an attractive and challenging topic which blooms various interesting applications in spatial-temporal databases. In this work, we study a new problem of searching trajectories by locations, in which context the query is only a small set of locations with or without an order specified, while the target is to find the k BestConnected Trajectories (k-BCT) from a database such that the k-BCT best connect the designated locations geographically. Different from the conventional trajectory search that looks for similar trajectories w.r.t. shape or other criteria by using a sample query trajectory, we focus on the goodness of connection provided by a trajectory to the specified query locations. This new query can benefit users in many novel applications such as trip planning. In our work, we firstly define a new similarity function for measuring how well a trajectory connects the query locations, with both spatial distance and order constraint being considered....