This paper deals with the multi-degree cyclic robotic cell scheduling problem with multiple parallel flow shop lines. The objective is to find the optimal sequence of robot operations aimed at maximizing the throughput. Considering our practical scenario, a robotic cell with a single dual-gripper robot and reentrant workstations is taken into consideration. We present a mixed-integer linear programming model for this problem and propose a hybrid particle swarm optimization algorithm (HPSO) with local search operators. Computational experiments are conducted by comparing with other two meta-heuristic algorithms. The results validate the effectiveness of the proposed algorithm. Based on the numerical analysis, we obtain the optimal assignment of parallel lines under the same operating conditions and help manufacturers achieve a good balance between processing capacity of workstations and robot serving capability.