Since the traffic administration at road intersections determines the capacity bottleneck of modern transportation systems, intelligent cooperative coordination for connected autonomous vehicles (CAVs) has shown to be an effective solution. In this paper, we try to formulate a Bi-Level CAV intersection coordination framework, where coordinators from High and Low levels are tightly coupled. In the High-Level coordinator where vehicles from multiple roads are involved, we take various metrics including throughput, safety, fairness and comfort into consideration. Motivated by the time consuming space-time resource allocation framework in [1], we try to give a low complexity solution by transforming the complicated original problem into a sequential linear programming one. Based on the "feasible tunnels" (FT) generated from the High-Level coordinator, we then propose a rapid gradient-based trajectory optimization strategy in the Low-Level planner, to effectively avoid collisions beyond High-level considerations, such as the pedestrian or bicycles. Simulation results and laboratory experiments show that our proposed method outperforms existing strategies. Moreover, the most impressive advantage is that the proposed strategy can plan vehicle trajectory in milliseconds, which is promising in realworld deployments. A detailed description include the coordination framework and experiment demo could be found at the supplement materials, or online at https://youtu.be/MuhjhKfNIOg.