This article proposes a commuted waveguide synthesis model for the geomungo, a Korean traditional plucked-string instrument featuring unusually wide vibrato. To model pitch fluctuation as well as the decay characteristics of its harmonic partials, a time-varying loss filter with a sinusoidal loop gain is used. Filter parameters are estimated by approximating the gains, and excitation signals are generated by inverse filtering the original sound. Real-time implementation of the algorithm for the development of the virtual instrument is also discussed.