Continuum solvation models have become a widespread approach for the study of environmental effects in Density Functional Theory (DFT) methods. Adding solvation contributions mainly relies on the solution of the Generalized Poisson Equation (GPE) governing the behavior of the electrostatic potential of a system. Although multigrid methods are especially appropriate for the solution of partial differential equations, up to now, their use is not much extended in DFT-based codes because of their high memory requirements. In this Article, we report the implementation of an accelerated multigrid solver-based approach for the treatment of solvation effects in the Vienna ab initio Simulation Package (VASP). The stated implicit solvation model, named VASP-MGCM (VASP-Multigrid Continuum Model), uses an efficient and transferable algorithm for the product of sparse matrices that highly outperforms serial multigrid solvers. The calculated solvation free energies for a set of molecules, including neutral and ionic species, as well as adsorbed molecules on metallic surfaces, agree with experimental data and with simulation results obtained with other continuum models.