In recent years, connected automated vehicles (CAVs) have attracted much attention, and the coordination strategy of CAVs in isolated intersections has been widely discussed. However, these algorithms for isolated intersections cannot be directly applied in a multi-intersection road network (MiRN). The coordination strategy in the MiRN requires further investigation. This paper proposes a two-tier strategy for CAV coordination in the MiRN. First, we analyze the coordination problem in isolated intersections and formulate it as a mixed-integer programming problem. Then, for the MiRN, we propose a consensus prediction method to estimate the travel time for CAVs with different paths. Finally, a novel coordination approach is given, showing how to determine the optimal path for CAVs. The experimental results demonstrate the efficiency of the proposed strategy under various traffic flow rates. Compared with the fixed signal time assignment method and the actuated signal time assignment method, our method reduces the average travel time by about 74−83% under different flow rates. We also evaluate the impact of parameters on the strategy’s performance and provide some suggestions for setting these parameters.