Multigrid algorithms for C⁰ interior penalty methods (which are discontinuous Galerkin methods) for fourth order problems will be discussed. We will show that the convergence behavior of the multigrid algorithms is similar to that for second order problems, provided that we use a smoothing scheme involving a Poisson solve as a preconditioner. Such a preconditioner can be easily implemented because the C⁰ finite element spaces are standard spaces for second order problems.