Under the Connected Vehicles (CV) environment, it is possible to create a Cooperative Vehicle Intersection Control (CVIC) system that enables cooperation between vehicles and infrastructure for effective intersection operations and management when all vehicles are fully automated. Assuming such a CVIC environment, this paper proposed a CVIC algorithm that does not require a traffic signal. The CVIC algorithm was designed to manipulate individual vehicles' maneuvers so that vehicles can safely cross the intersection without colliding with other vehicles. By eliminating the potential overlaps of vehicular trajectories coming from all conflicting approaches at the intersection, the CVIC algorithm seeks a safe maneuver for every vehicle approaching the intersection and manipulates each of them. An additional algorithm was designed to deal with the system failure cases resulting from inevitable trajectory overlaps at the intersection and infeasible solutions. A simulation-based case study implemented on a hypothetical four-way single-lane approach intersection under varying congestion conditions showed that the CVIC algorithm significantly improved intersection performance compared with conventional actuated intersection control: 99% and 33% of stop delay and total travel time reductions, respectively, were achieved. In addition, the CVIC algorithm significantly improved air quality and energy savings: 44% reductions of CO 2 and 44% savings of fuel consumption.