Video-processing technology was used to acquire detailed spatio-temporal data of pedestrians, and the underlying law of the conflict between violating pedestrians and turning vehicles was analyzed, then a model of pedestrians' crossing position distribution was proposed. First, on the basis of the survey data, the relationship between conflict and pedestrian crossing distribution was qualitatively analyzed. Then, based on the analysis of pedestrians' crossing positions at seven surveyed crosswalks, the impacts of crosswalk length and elapsed time on pedestrians' crossing position distribution were investigated. Further, a Gauss function was applied to model the pedestrians' crossing position distribution at different times. Finally, the formulas about elapsed time, crosswalk length and three model parameters were established. The adjusted R2 of the fitting models were 0.9, 0.93 and 0.97 respectively, which indicates that the proposed models can well represent the law of pedestrians' crossing position distribution. The proposed model was verified and the role of the model on determining the conflict zone was illustrated. An optimization method to reduce the conflict zone was put forward.