A metal film coupled with a metal nanoparticle is a simple and stable nanoantenna structure with plasmonic characteristics. This film-coupled nanoparticle system also has potential for the signal enhancement due to the highly confined field between the film and the nanoparticle. Recently, this structure has been used to probe the limit of the enhanced field and the interaction with quantum emitters. The well-known mode in this nanoantenna structures is the gap dipole mode. However, the high order modes become significant when the gap between the nanoparticle and the film is reduced. In this work, the high order modes are investigated. The size of the whole nanoantenna structure is around λ/10. In experiments, the far field scattering spectra/images under different excitation and collection conditions indicate the influence and the existence of the high order modes. The calculated far-field scattering spectra and spatial intensity profiles have good agreement with the experimental results. In addition, among these high order modes, the simulated near-field distributions reveal distinguishable features which include the different symmetry of field distributions and the various size of confined field. The investigation of these high order modes may provide the information for designing the interaction between this nanoantenna structure and other plasmonic devices.