A simple magnetic modulation structure of the exchange-coupling FePt/FeNi bilayer film is fabricated and studied for its magnetization dynamics using time-resolved magneto-optical polar Kerr spectroscopy. It is found that two spin-wave modes can be excited. One is fixed at ∼3.2 GHz in frequency for any external field and may serve as a frequency-stabilized spin-wave filter, while the other is external field dependent. In contrast, only the external field-dependent mode is excited in single-layer FeNi, supporting the localized origin of the mode at ∼3.2 GHz, which is confined to a thin exchange-coupling region. The other external field-dependent mode in frequency is attributed to the Kittel mode.