In this paper a preconditioner for a numerical global circulation ocean model is presented. Starting from the discretization of an elliptic Laplace problem the associated linear system is solved by means of the Preconditioned Conjugate Gradient Method (PCG). In this work, we observe that the performance of the PCG solver depends on the grid resolutions and the Laplace coefficients. To address these problems we propose a new preconditioning technique. Finally, an implementation of the PCG solver with an inverse built "ad-hoc" preconditioner on multi-core GPU architecture is proposed.