To address the flexible workshop scheduling problem of automated guided vehicles (AGV), a scheduling model was established with the objective of minimizing the makespan of handling machines, i.e., the completion time of the scheduling system. A gray wolf neighborhood algorithm based on a greedy strategy was designed to solve this problem. In the initialization stage, vectors of a certain length were randomly generated and transformed into feasible process and machine codes through the LPV method. Under the greedy strategy, the AGV with the shortest completion time was selected to generate the handling machine code. The gray wolf operator was adopted to update the random vector, and the IPOX of the genetic algorithm and the uniform crossover operator were introduced to cross the process and machine codes. During neighborhood search, one-stage optimization (1-opt) and two-stage optimization (2-opt) were designed to further optimize the operation and machine codes. According to the elite strategy, half of the individuals were retained for the next iteration, and the scheduling result was obtained when the algorithm terminates. The algorithm efficiency was verified through the comparison of solutions by multiple algorithms under the same parameters in 20 examples and the comparison of solutions by a single example under adjusted parameters. The results show that the improved algorithm can effectively solve the AGV scheduling problem, and its solution performance is superior to that of other algorithms.