Domain Adaptation (DA) is a technique that aims at extracting information from a labeled remote sensing image to allow classifying a different image obtained by the same sensor but at a different geographical location. This is a very complex problem from the computational point of view, specially due to the very high-resolution multispectral images. TCANet is a deep learning neural network for DA classification problems that has been proven as very accurate for solving it. TCANet consists of several stages based on the application of convolutional filters obtained through Transfer Component Analysis (TCA) computed over the input images. It does not require training, in contrast to the usual CNN-based networks. In this paper, a hybrid parallel TCA-based domain adaptation technique for solving the classification of very high-resolution multispectral images is presented. It is designed for efficient execution on a multi-node computer by using message passing interface (MPI), exploiting the available Graphical Processing Units (GPUs), and making efficient use of each multicore node by using Open Multiprocessing (OpenMP). As a result, an accurate DA technique from the point of view of classification and with high speedup values over the sequential version is obtained, increasing the applicability of the technique to real problems.