Music therapy is a common method to relieve anxiety and pain in cancer patients after surgery in recent years, but due to the lack of technical and algorithmic support, this therapy is not particularly stable and the therapeutic effect is not good. In this study, a neural network robotic system based on breast cancer patients was designed to analyze the effect of music relaxation training on alleviating adverse reactions after chemotherapy in breast cancer patients. Firstly, this paper introduces the necessity of neural network robot system research under the background of music therapy, and then summarizes the positive effect of music relaxation therapy on alleviating adverse reactions after chemotherapy in breast cancer patients, finally, uses neural network robot system to construct music therapy system. The experimental results show that the new music therapy proposed in this study has a good effect in alleviating the adverse reactions of breast cancer patients after chemotherapy, and the cure rate is increased by 7.84%. The research results of this paper provide reference for the next development of neural network robot system in the medical field.