The Helmholtz equation is widely used as a model problem in many fields where indefinite partial differential equations arise. Therefore, it is very interesting to develop fast solvers for this equation. However, this is very challenging due to its indefinite character. With this in mind, a truly shifted Laplacian preconditioner is presented. It is based on multigrid, as multigrid iterations are used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix are validated with local Fourier analysis. Multigrid analysis results are verified by numerical experiments.