The urgency of the discussed issue is caused by the need to provide software for tracking objects in real time. The main aim of the study: to create an object-tracking algorithm in the frame in real time. The methods used in the study: parallel implementation of the sigmoid neural network on the GPU, measuring the temporal characteristics of the parallel algorithm and its optimization. The results: The authors have proposed implementation of a neural network algorithm on graphic processor (GPU) for tracking an object in a video frame. The specific character of the algorithm is the use of a training set which establish correspondence between the video frame and the object center coordinates in this frame when training a neural network. Owing to GPU application the tracking problem can be solved in real time (25 frames per second) at the processed frame sizes up to 1280×960. The algorithm is based on the use of multilayer perceptron and has a number of parameters, which are determined experimentally. One of such parameters is the number of the hidden layer neurons. Due to the algorithm implementation on GPU the authors considered the number of neurons multiple 16. It was determined experimentally that 16 and 32 neurons cannot provide even a small degree of memorizing images, 48 neurons cope with learning only small training samples, and 64 neurons provided a good degree of memorizing images and speed. Further increase in the number of neurons results only in reducing speed of the neural network functioning and its training. The frequency which is required for taking pictures from a video to train effectively a neural network is worth noticing as well. It is found out experimentally that at a sampling rate of one frame of ten, the sum of the maximum deviations in coordinates is 50, when the object size is 300×300; further increase of the frame rate slows down the process of training without significant gain in quality. The authors obtained the tracking accelerating by 10 times in comparison with the CPU of a personal computer. The neural network training is accelerated only 2 times on average. This is caused by the need to transpose the weight matrices when implementing the neural network training on the GPU. To implement the parallel algorithm, the hardware and software architecture CUDA is used. It allows computation on graphics processors NVIDIA, supporting GPGPU technology (general purpose computations on GPU). For preliminary image processing and data output the computer vision library OpenCV is used.