This paper examines the impact of frequency-modulated (FM) signals on vibrational resonance (VR) in a position-dependent mass (PDM)–Duffing oscillator system. FM signals are categorized into two types: narrow-band FM (NBFM) and wide-band FM (WBFM). We conduct a numerical study to analyze the effects of both FM signals on the system. The occurrence of VR is investigated not only based on signal parameters (g,ω,Ω) but also considering the contributions of PDM parameters (m0,λ). In addition to various dynamic phenomena such as period-doubling bifurcation, reverse period-doubling bifurcation, chaos, and attractor crises, our numerical simulations reveal several noteworthy observations. These include the emergence of multiple resonance peaks, the absence of response amplitude decay, the presence of hysteresis, and a jump phenomenon induced by the FM signal. By delving into phase portraits, bifurcation diagrams, trajectory plots, and resonance plots, we elucidate the underlying resonance mechanisms and provide insights into the distinctive features of the resonance curve.