  AC Josephson current density in a Josephson junction with DC bias is
spatially modulated by an external magnetic field, and induces an
electromagnetic (EM) field inside the junction. The current-voltage ($I$-$V$)
curve exhibits peaks due to the resonance between the EM field and the
spatially modulated AC Josephson current density. This is called {\it Fiske
resonance}. Such a spatially modulated Josephson current density can be also
induced by a non-uniform insulating barrier and the Fiske resonance appears
without external magnetic field. This is called zero-field Fiske resonance
(ZFFR). In this paper, we theoretically study the ZFFR coupled with spin-waves
in a superconductor/ferromagnetic insulator/superconductor junction
(ferromagnetic Josephson junction) with a non-uniform ferromagnetic insulating
barrier. The resonant mode coupled with spin-waves can be induced without
external magnetic field. We find that the $I$-$V$ curve shows resonant peaks
associated with composite excitations of spin-waves and the EM field in the
junction. The voltage at the resonance is obtained as a function of the normal
modes of EM field. The ZFFRs coupled with spin-waves are found as peak
structures in the DC Josephson current density as a function of bias voltage.
