In an elastic-wave filter device that includes a band-pass filter and a band-eliminate filter connected to the band-pass filter, insertion loss in a pass band is significantly reduced and attenuation in a stop band is significantly increased. The elastic-wave filter device has a pass band and a stop band at frequencies higher than the pass band. The band-pass filter and the first band-eliminate filter are connected in series between an input terminal and an output terminal. A first parallel-arm resonator of the first band-eliminate filter includes a first resonance frequency in the stop band. A second parallel-arm resonator includes a second resonance frequency in the stop band, the second resonance frequency being higher than the first resonance frequency. An impedance value of the first parallel-arm resonator is larger than an impedance value of the second parallel-arm resonator.