Summary: We prove the existence of a renormalized solution for the nonlinear elliptic problem \[ -\text{div } a(x, u, \nabla u) - \text{div } \phi(u) + g(x, u, \nabla u) = f \text{ in }\Omega, \] in the setting of Musielak-Orlicz spaces. \(\phi \in \mathcal C^0 (\mathbb R, \mathbb R^N)\), the nonlinearity \(g\) has a natural growth with respect to its third argument and satisfies the sign condition while the datum \(f\) belongs to \(L^1 (\Omega)\). No \(\Delta_2\)-condition is assumed on the Musielak function.