The occurrence of vibrational resonance (VR) in a dual-frequency-driven multistable system with a spatially varying mass modelling particle with position-dependent mass (PDM) and evolving in a one-dimensional symmetric periodic potential has been investigated and reported in this paper. We numerically compute and analyze the response amplitude, the effects of the PDM parameters (m 0, a) on the potential structure, the occurrence of VR and the bifurcation of the equilibrium points. It is shown that the PDM parameters, besides controlling VR, can induce unconventional resonance patterns through the variation of the potential well depth. The resonant states can be influenced through the cooperation of the PDM parameters and the external forcing leading the system from multiresonance state into single and double resonance states. The contributions of the fixed rest mass m 0 on the VR and the PDM-induced resonance are determined by threshold conditions imposed by the magnitude of the mass nonlinear strength a.