This paper is an attempt to combine a full multigrid (FMG) algorithm with the classical anisotropic mesh adaptation loop. The FMG algorithm aims at improving the convergence rate of the flow solver, while mesh adaptation tends to improve the tradeoff between CPU time and accuracy of the solution. Coupling these two methods consists, at each stage of the adaptation loop, in running a multigrid simulation using the previously adapted coarser meshes. The main benefits of this coupling are that (i) the convergence of mesh adapta-tion is improved thanks to the properties stated by the FMG theory, and (ii) anisotropic coarsening is automatically handled by mesh adaptation. First, the implementation and the validation of the multigrid procedures are described, and then the coupling is detailed. Results are presented in 2D and 3D for various flow prescriptions, including a real-life configuration.