This paper introduces a new approach for Autonomous Intersection Management (AIM) for isolated, non-signalized intersections. AIM is an innovative concept for managing autonomous and connected vehicles at an intersection. In this approach, a local Intersection Manager (IM) gives each vehicle the right-of-way to pass through the intersection. The main goal is to minimize either the total travel time or the total energy consumption in an intersection. The IM uses a priority-based intersection management approach to determine the right-of-way of the incoming vehicles. A reservation-based strategy is implemented together with a set of rules called Compatible Stream Groups (CSGs) which are inherently safe to achieve fail-safety. To compare and evaluate the efficiency of our proposed approach, two alternative traffic management systems were implemented for comparison: a conventional traffic light system and a first-come-first-served policy. The proposed approach is compared with these two policies using driving scenario-based test cases. The simulation results show that our approach can be used to increase the traffic flow or decrease energy consumption without compromising safety.