Actual manufacturing enterprises usually solve the production blockage problem by increasing the public buffer. However, the increase of the public buffer makes the flexible flow shop scheduling rather challenging. In order to solve the flexible flow shop scheduling problem with public buffer (FFSP–PB), this study proposes a novel method combining the simulated annealing algorithm-based Hopfield neural network algorithm (SAA–HNN) and local scheduling rules. The SAA–HNN algorithm is used as the global optimization method, and constructs the energy function of FFSP–PB to apply its asymptotically stable characteristic. Due to the limitations, such as small search range and high probability of falling into local extremum, this algorithm introduces the simulated annealing algorithm idea such that the algorithm is able to accept poor fitness solution and further expand its search scope during asymptotic convergence. In the process of local scheduling, considering the transferring time of workpieces moving into and out of public buffer and the manufacturing state of workpieces in the production process, this study designed serval local scheduling rules to control the moving process of the workpieces between the public buffer and the limited buffer between the stages. These local scheduling rules can also be used to reduce the production blockage and improve the efficiency of the workpiece transfer. Evaluated by the groups of simulation schemes with the actual production data of one bus manufacturing enterprise, the proposed method outperforms other methods in terms of searching efficiency and optimization target.