This paper presents a semi-implicit numerical method for the simulation of grain growth in two dimensions with a multi phase field model. To avoid the strong stability condition of traditional explicit methods, a first-order, semi-implicit discretisation scheme is employed, which offers a good compromise with regard to memory intensity and computational requirements. A nonlinear multigrid solver based on the Full Approximation Scheme is implemented to solve the equations resulting from this discretisation. Simulations with the multigrid solver show that the solver has grid size independent convergence properties and is faster than a standard first-order explicit solver. To validate the implementation, the results of specific test cases are studied.