In this paper, we investigate the existence of normalized ground state solutions for a class of quasilinear elliptic equations. More precisely, we consider the p-Laplace equation with a prescribed $L^p$-norm constraint. The problem involves a potential function and a nonlinear term with mass supercritical growth. By employing variational methods, we aim to find solutions with a given mass, where the parameter $\lambda$ appears as a Lagrange multiplier. Under appropriate assumptions of potential and nonlinearity, we establish the existence of such solutions for any given positive mass.