Accurate pedestrian crossing intention prediction is critical for autonomous vehicles and advanced driver assistance systems. In multi-pedestrian and multi-vehicle interaction scenes, the social interaction between pedestrians and other traffic participants is ubiquitous, which affects pedestrian crossing decisions and the accuracy of prediction. However, previous studies on pedestrian crossing intention lack comprehensive consideration and mathematical modeling of the social interaction. We propose a “social interaction force” (SIF) to identify and quantify social interaction behaviors and combine the hidden Markov model (HMM) to predict pedestrian crossing intentions 1.0 s ahead. Firstly, a large dataset of pedestrian-vehicle interaction samples is collected from two views, and high-dimensional features are extracted for pedestrian intention prediction. Next, the concept of SIF is proposed to quantitatively characterize the influence of other pedestrians and vehicles on pedestrian crossing decisions, including “pedestrian interaction force” and “pedestrian-vehicle interaction force.” Finally, SIF, pedestrian features, and road structure features are input into HMM. Sliding time windows are applied to the HMM to achieve dynamic prediction of pedestrian intention sequences. Experimental results show that the recognition accuracy of the proposed model is 0.976, and the accuracy of 1.0 s ahead prediction is 0.932 with guaranteed prediction speed. The proposed model performance is superior to that of the most prevalent models developed thus far.