It is shown that a superlens with unmatched dielectric medium (termed as "unmatched superlens", UMSL) can enable super-resolution imaging in a broad frequency range. The broadband UMSL comprises dielectric-metal-dielectric layers with appropriately designed thickness. Numerical simulations demonstrate that the deficiency of imaging due to the mismatched permittivity of the metal and dielectric can be improved with the existence of two waveguide modes of the UMSL structure. The frequency band and quality of super resolution imaging are mainly determined by the two modes, which deliver the amplitude and phase modulation of transmitted evanescent waves in a wide transversal wavenumber range.