Accurate driving risk assessments are essential in vehicle collision avoidance and traffic safety. The uncertainty in driving intentions and behavior, coupled with the difficulty in accurately predicting future trajectories of vehicles, poses challenges in assessing collision risk among vehicles. Existing research on collision risk assessment has been limited to focusing on pre-crashes (e.g., time-to-collision) and ignoring the impact of crash severity on risk. Research integrating pre- and post-crash is needed to assess the collision risk comprehensively. Therefore, the objective of this study was to propose an assessment model for collision risk in a vehicle-to-vehicle communication environment to achieve a more scientific assessment of driving risk by integrating probability (pre-crash) and intensity (post-crash). The proposed trajectory prediction model takes driving intentions into account and employs a social tensor pool to integrate interactions between vehicles, thereby achieving improved prediction accuracy. The likelihood of collision is obtained by analyzing the conflict relationship between the predicted and candidate trajectories of different vehicles. This study proposes a risk assessment model comprising two parts: one assesses the likelihood of collision by analyzing the conflicted relationship between predicted and candidate trajectories of different vehicles, and the other determines collision intensity through analysis of vehicle driving states. Finally, publicly available unmanned aerial vehicle (UAV)-based traffic data are used to validate the models. The prediction errors of the proposed trajectory prediction model for three-second trajectories are 0.68 m and 1.34 for the root mean square error and negative log-likelihood, respectively. The quantitative experimental results illustrate that the proposed model outperforms existing models and can scientifically assess the risk of vehicle travel.