In this work, a coordinate solver for elastic net regularized logistic regression is proposed. In particular, a method based on majorization maximization using a cubic function is derived. This to reliably and accurately optimize the objective function at each step without resorting to line search. Experiments show that the proposed solver is comparable to, or improves, state-of-the-art solvers. The proposed method is simpler, in the sense that there is no need for any line search, and can directly be used for small to large scale learning problems with elastic net regularization.