In this study, the Volterra lattice system is investigated as a semi-discrete version of the modified KdV equation. Finding exact solutions for this system is challenging due to its applications in understanding nonlinear phenomena in physics and engineering. In this work, we study the generalised exponential rational function approach (GERFA) to extract exact traveling wave solutions of the Volterra lattice system (VLS). The proposed method provides promising results that allow us to investigate different types of solutions in Volterra lattice systems.