By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem. By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. The only source for the wave superposition method, the unique solutions for all wave numbers can be ensured. equal to that of the standard wave superposition method, but also the accuracy is much higher than with correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculating show that the present method can effectively overcome the non -uniqueness problem.