Automated guided vehicles (AGVs) in the U-shaped automated container terminal travel longer and more complex paths. The conflicts among AGVs are trickier. The scheduling strategy of the traditional automated container terminal is difficult to be applied to the U-shaped automated container terminal. In order to minimize the handling time of all tasks and avoid AGV conflicts simultaneously in the U-shaped automated container terminal, this paper establishes a hybrid programming model for conflict-free integrated scheduling of quay cranes, AGVs, and double-cantilever rail cranes in the unloading process. It consists of a discrete event dynamic model and a continuous time dynamic model. An improved genetic seagull optimization algorithm (GSOA) is designed. A series of numerical experiments are conducted to verify the effectiveness and the efficiency of the model and the algorithm. The results show that the proposed method can simultaneously realize the AGVs collision avoidance and multi-equipment integrated scheduling optimization in the U-shaped automated container terminal.