In this paper, we investigate systems of nonlinear fourth-order Emden-Fowler type equations. We employ the variational iteration method (VIM) for solving these systems of equations. The newly developed fourth-order Emden-Fowler equation is characterized by three types, where the shape factor appears three times, twice, and once for the first type, second type, and the third type respectively. We use distinct Lagrange multipliers for these specific types to overcome the singularity at the origin. We solve several numerical examples obtaining a rapidly convergent sequence of approximations. In all examples investigated, we achieved approximations with a high level of accuracy, thus confirming that we can get accurate approximations with few variational iterations.