Accurate vehicle speed prediction leads to reduced energy consumption and increased safety of intelligent vehicles. Considering the data available in intelligent transportation systems and the capability of deep neural networks to exploit these data, an intelligent method for speed prediction using deep neural networks is proposed. Speed prediction is performed using the speed history of the target vehicle and its preceding vehicles. In order to increase prediction accuracy, an innovative method for normalizing vehicle speed data is introduced, which results in a reduction in prediction error. Furthermore, to address practical driving challenges, uncertainty in the amount of available speed history and the number of preceding vehicles is considered in the developed method. In this study, speed prediction is carried out with a very short time step, which, although it improves accuracy, increases the dimensionality of the problem and doubles the difficulty of the prediction task; an issue that has not been reported in previous studies. Real-world highway data are used to train the intelligent speed prediction models. The results show that the proposed method achieves higher accuracy, particularly in the initial time steps, and is free of offset. The mean absolute prediction error over a six-second horizon obtained using the proposed method is 0.2410 m/s, which indicates at least a 49.1% reduction compared to analytical models.