Vehicle speed prediction can benefit a wide range of vehicle control designs, especially for fuel economy applications. This paper shows a computationally light vehicle short term speed predictor designed for on-board implementation, using minimal information of speed measurement only. The predictor generalizes historical speed data's underlying pattern and predicts from probability aspect. One novelty of the method is the usage of fuzzy modeling to eliminate the resolution limitation in vehicle acceleration state definition, classification, and prediction. The method uses Auto-regressive (AR) model to capture vehicle speed data's short term dynamics, and classifies the data into multiple acceleration states by fuzzy membership. In the prediction process, acceleration measurements are mapped to the Markov states by fuzzy encoding, and future acceleration states are predicted by Markov transition. Deterministic speed prediction is calculated from the trained AR models, which are selected by fuzzy state membership similarity. The developed predictor is tested with a vehicle's real urban driving data, and the effectiveness of the incorporated techniques is verified by a comparison study.