Vehicle trajectory data can reveal actual driving behavior patterns reflected by different road geometric designs, providing important insights for road safety analysis and improvements. This study aims to is to explore the correlation between vehicle trajectory fractal dimension (FD) and highway crash rate (CR) using large-scale telematics trajectory data. Specifically, we propose three methods to measure the FD of vehicle trajectories, and developed fractal parameter estimation technology. The results show that FD differences between road segments have a statistically significant effect on CR. A comparison of FD with five common surrogates in identifying high-risk crash sections reveals that FD reduces the false alarm rate from 52% to 94% (other surrogates) to 46%, with a recall rate of 95%. The fractal method enhances the dimensionality of trajectory feature analysis, refining the granularity of road safety analysis. It fully considers the interaction between road geometry design and driving behavior, revealing the complex dynamic movement of vehicles within the road system. This study provides methodological support for improving road geometry design and enhancing road safety.