Reliable motion prediction of surrounding vehicles is the key to safe and efficient driving of autonomous vehicles, especially at urban intersections with complex traffic environments. This study models driving intentions and future driving speeds at urban intersections and improves model prediction performance by considering traffic environment characteristics. Key feature parameters including environmental characteristics are first extracted through driving behavior analysis and existing research experience. Then models with different input combinations are constructed to explore the effectiveness of different factors in predicting driving intention and future speed. In particular, in vehicle speed modeling, a target detection algorithm is used to identify traffic participants. Based on the identified traffic participant and vehicle position information, a new method for speed prediction that can reflect the dynamic interaction characteristics between the driver and the traffic environment is proposed. Models are trained and tested using natural driving data from China. Finally, the models with the simplest input and the best effect are determined. The driving intention recognition model can accurately predict the driving maneuvers of straight-Ahead, stopping, turning left and right 4 seconds before reaching the intersection. The speed prediction model can significantly improve the speed prediction accuracy, and shows stronger robustness and adaptability than existing models. This research provides important technical support for developing intelligent driving systems suitable for complex urban traffic environments.