The Graphics Processing Units (GPUs) have been used for accelerating graphic calculations as well as for developing more general devices. One of the most used parallel platforms is the Compute Unified Device Architecture (CUDA), which allows implementing in parallel multiple GPUs obtaining a high computational performance. Over the last years, CUDA has been used for the implementation of several parallel distributed systems. At the end of the 80s, it was introduced a type of Neural Networks (NNs) inspired of the behavior of queueing networks named Random Neural Networks (RNN). The method has been successfully used in the Machine Learning community for solving many learning benchmark problems. In this paper, we implement in CUDA the gradient descent algorithm for optimizing a RNN model. We evaluate the performance of the algorithm on two real benchmark problems about energy sources. In addition, we present a comparison between the parallel implement in CUDA and the traditional implementation in C programming language.