In this paper, we will be concerned with the existence of renormalized solutions to the following parabolic-elliptic system ∂u ∂t + Au = σ(u)|∇φ|2 in QT = Ω × (0,T), −div(σ(u)∇φ) = divF(u) in QT, u = 0 on ∂Ω × (0,T), φ = 0 on ∂Ω × (0,T), u(·, 0) = u0 in Ω, where Au = −div a(x, t,u,∇u) is a Leray-Lions operator defined on the inhomogeneous Orlicz-Sobolev space W1,x0 LM(QT) into its dual, M is a N-function related to the growth of a. M does not satisfy the ∆2-condition, and σ and F are two Carathéodory functions defined in QT ×R.