The authors study the convergence behaviour of multigrid algorithms for interior penalty methods for second order elliptic boundary value problems. It is proved that the convergence factor of the multigrid algorithms with \(V\)-, \(F\)-, or \(W\)-cycle and \(m\) pre- and \(m\) post-smoothing steps is independent of the number of grid levels if the number of smoothing steps is sufficiently large. The norm of the error propagation operator of the multigrid algorithms is bounded above by \(C/m^\alpha\), where \(C\) is a positive constant independent of the number of grid levels and \(\alpha\) is the index of elliptic regularity. Numerical experiments confirm the theoretical results.