In this paper, we present a hierarchical distributed coordination strategy for connected and automated vehicles (CAVs) that are travelling through multiple unsignalized intersections. The control strategy focuses on the improvement of vehicle fuel efficiency and system mobility. In presence of wireless communication among the involved CAVs and the intersection controllers, our coordination strategy focuses on leading the CAVs travel through a road network without conventional traffic light control and ensuring collision avoidance at the intersection areas. We propose a three-layered coordination strategy in this paper. First, we evaluate the road desired average velocity considering both upstream and downstream traffic to speed up the traffic density balance. Second, the intersection controllers optimally assign reference velocity to each vehicle based on the minimization of velocity deviation from its current velocity and collision avoidance at the intersections. Finally, fast model predictive control (F-MPC) is applied for each vehicle to track their reference velocity in a computationally efficient manner. Two simulation scenarios with different difficulty levels have been implemented on a two-interconnected intersection network. Simulation results indicate the feasibility and scalability of the proposed method, as well as vehicle fuel efficiency and system mobility improvement.