For vehicles, knowledge of the complete route characteristics at the beginning of a trip is beneficial for improving the driving safety, mobility, and energy efficiency. However, prediction of vehicle speed is difficult due to limited information about driver behaviors and traffic flow. In this paper, an iterative optimization algorithm for vehicle speed prediction is proposed. First, the global speed is predicted based on historical data, utilizing multiple Gaussian process regression (GPR) for different driving styles. Then the multiple GPR sub-models are integrated adaptively by learning from the real driving scenarios. A local speed prediction algorithm for a few seconds ahead is developed based on the long short-term memory (LSTM) neural network. Finally, the local and global prediction results are fused to form compound speed by the Markov transition probability matrix. The proposed algorithm is validated in experiments over to a 300 meters route ahead of a traffic light. Results show that the proposed solution can gradually improve the prediction performance, and up to 70.67% reduction in prediction error can be achieved relative to conventional GPR based solution.