In the aerospace field, there are many curved surface workpieces that need friction stir welding. Industrial robots provide an attractive choice for friction stir welding of three-dimensional space curves, but the huge axial force in the process of friction stir welding puts forward high requirements for the axial stiffness of the stirring head of industrial robots. In order to improve the axial stiffness of the stirring head of the robot during friction stir welding, a workpiece position optimization method based on the optimal stiffness interval is proposed. Firstly, the stiffness database of parallel/series mechanism of hybrid robot was constructed to reduce the stiffness calculation time. Secondly, based on the axial stiffness of the robot stirring head, the concept of the optimal stiffness interval was proposed as the optimization index. Moreover, considering singularity free, joint limit, joint continuity and workspace constraints, the workpiece position optimization algorithm based on the optimal stiffness interval was studied. Finally, the method is verified by simulation and experiment. The results show that this method can make the robot always maintain the position and posture with better stiffness in the direction of the stirring head axis by optimizing the position of the workpiece, so as to significantly increase the welding stiffness of the robot in the welding process.