Although several safety countermeasures such as reforming intersection layouts have been implemented, methods to quantitatively evaluate their effects prior to the installation have not yet been established. One of the most important safety issues at signalized intersections is the interaction between left-turning vehicles (left-hand traffic) and pedestrians/cyclists. This paper aims to analyze and model the trajectory variations of left-turning vehicles considering intersection geometric characteristics and the interaction with other users. Such variations in vehicle trajectories reflect the difference in driver behavior which may lead to misunderstanding of other users' decisions further resulting in collisions. Vehicle trajectories are collected at several signalized intersections with various traffic and geometric characteristics by video observations. The analysis reveals a significant variation in trajectories depending on intersection angle, number of exit lanes and vehicle type. For modeling individual vehicle trajectories, this paper applies the Euler-spiral-based approximation methodology. Furthermore, trajectory distribution is modeled by empirically estimating the distribution of trajectory parameters. Model validation showed that estimated trajectory distributions explain well the spatial maneuver of left-turning vehicles.