Numerical simulations of coupled fluid-rigid solid problems by multigrid fictitious boundary and grid deformation methods are presented. The flow is computed by a special ALE formulation with a multigrid finite element solver. The solid body is allowed to move freely through the computational mesh which is adaptively aligned by a special mesh deformation method such that the accuracy for dealing with the interaction between the fluid and the solid body is highly improved. Numerical examples are provided to show the efficiency of the presented method.