The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$
-operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,
 $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz
spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined from $W^{1}_{0}L_{M}(Omega)$ into its dual,
$Phi in C^{0}(mathbb{R},mathbb{R}^{N})$. The function $g(x,u,nabla u)$ is a non linear lower
 order term with natural growth with respect to $|nabla u|$, satisfying the sign condition and the
 datum $mu$ is assumed belong to $L^1(Omega)+W^{-1}E_{overline{M}}(Omega)$.