With the increasing prevalence of location sensor devices like GPS, it has been possible to collect large datasets of a special type of spatio-temporal data called trajectory data. A trajectory is a discrete sequence of positions that a moving object occupies in space as time passes. Such large datasets enable researchers to study the behavior of the objects describing these movements by issuing spatial queries. Among the queries that can be issued are top-K trajectory similarity queries, which retrieve the K most similar trajectories to a given query trajectory. This query has applications in many areas, such as urban planning, ecology and social networking; however, this query is computationally expensive. In this work, we introduce a new parallel top-K trajectory similarity query technique for GPUs, FastTopK, to deal with these challenges. Our experiments on two large real-life datasets showed that FastTopK produces on average 107.96X smaller candidate result sets, and 3.36X faster query execution times than the existing state-of-the-art technique, TKSimGPU.