This paper describes a new approach of the Multilevel method studied in \citenat2 and \citenat1, in order to solve the 2D Laplace equation. The first approach of the multilevel method is a multiplicative or serial method since each level is addressed sequentially~; it presents, as MG methods, a mesh-independent convergence rate. It is more costly than MG methods, but easier to implement. In order to smooth all the frequency components of the error, the V-cycle strategy is used and it results in several cost functional evaluations per cycle. In this paper, the proposed strategy is based on an additive approach. A preconditionner is deduced from this multilevel method, which provides a better efficiency than the previous method since all frequencies are addressed at the same time, while only one optimization iteration is needed. Furthermore, this method still presents a mesh-independent convergence rate.