The strong interaction between light and matter is one of the current research hotspots in the field of nanophotonics, and provides a suitable platform for fundamental physics research such as on nanolasers, high-precision sensing in biology, quantum communication and quantum computing. In this study, double Rabi splitting was achieved in a composite structure monolayer MoS2 and a single Ag@Au hollow nanocube (HNC) in room temperature mainly due to the two excitons in monolayer MoS2. Moreover, the tuning of the plasmon resonance peak was realized in the scattering spectrum by adjusting the thickness of the shell to ensure it matches the energy of the two excitons. Two distinct anticrossings are observed at both excitons resonances, and large double Rabi splittings (90 meV and 120 meV) are obtained successfully. The finite-difference time domain (FDTD) method was also used to simulate the scattering spectra of the nanostructures, and the simulation results were in good agreement with the experimental results. Additionally, the local electromagnetic field ability of the Ag@Au hollow HNC was proved to be stronger by calculating and comparing the mode volume of different nanoparticles. Our findings provides a good platform for the realization of strong multi-mode coupling and open up a new way to construct nanoscale photonic devices.