Object tracking refers to the relocation of specific objects in consecutive frames of a video sequence. Presently, this visual task is still considered an open research issue, and the computer science community attempted solutions from the standpoint of methodologies, algorithms, criteria, benchmarks, and so on. This article introduces a GPU-parallelized swarm algorithm, called the Honeybee Search Algorithm (HSA), which is a hybrid algorithm combining swarm intelligence and evolutionary algorithm principles, and was previously designed for three-dimensional reconstruction. This heuristic inspired by the search for food of honeybees, and here adapted to the problem of object tracking using GPU parallel computing, is extended from the original proposal of HSA towards video processing. In this work, the normalized cross-correlation (NCC) criteria is used as the fitness function. Experiments using 314 video sequences of the ALOV benchmark provides evidence about the quality regarding tracking accuracy and processing time. Also, according to these experiments, the proposed methodology is robust to high levels of Gaussian noise added to the image frames, and this confirms that the accuracy of the original NCC is preserved with the advantage of acceleration, offering the possibility of accelerating latest trackers using this methodology.